Consider the following. f(x) = x5 − x3 + 6, −1 ≤ x ≤ 1 (a) Use a graph to find the absolute maximum and minimum values of the function to two decimal places. maximum minimum (b) Use calculus to find the exact maximum and minimum values. maximum minimum

Answer:

[tex]A(x)=\$5,000(1.04)^{x}[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nx}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

x is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]P=\$5,000\\ r=0.04\\n=12[/tex]  

substitute in the formula above  

[tex]A(x)=\$5,000(1+\frac{0.04}{12})^{12x}[/tex]  

[tex]A(x)=\$5,000(\frac{12.04}{12})^{12x}[/tex]  

[tex]A(x)=\$5,000(1.04)^{x}[/tex]  

Answer:

  the zeros are x ∈ {-3, 1/2, 2}

Step-by-step explanation:

A graphing calculator shows where the zeros are. (See attached)

These suggest factors of (x +3)(x -2)(2x -1). To verify these are the factors, we can multiply this out to get ...

  = (x^2 +x -6)(2x -1)

  = 2x^2 +2x^2 -12x -x^2 -x +6

  = 2x^3 +x^2 -13x +6 . . . . same as the original expression

Answer:

  Distributive property

Step-by-step explanation:

The distributive property tells you ...

  a(b+c) = ab +ac

Here, you have a=4, c=2, so ...

  4(b+2) = 4·b + 4·2 = 4b +8

Answer:

Below

Step-by-step explanation:

a(b+c) = ab +ac

4(b+2) = 4·b + 4·2 = 4b +8

Which is distributive property!

mark me as brainliest!

thanks!

Answer:

  24

Step-by-step explanation:

Mack can choose any of the 4 for the first visit, any of the remaining 3 for the second visit, either of the remaining 2 for the third visit, then visit the last one. There are 4·3·2·1 = 24 ways Mack can do this.

_____

The number 4·3·2·1 is "four factorial", written as 4! (with an exclamation point). It is the number of ways 4 objects can be ordered, called the number of permutations of 4 objects.

Answer:

Step-by-step explanation:

The "fundamental theorem of algebra" says a polynomial of degree n will have n zeros. If the polynomial has real coefficients, the complex zeros will appear in conjugate pairs.

The graph of this quadratic (degree = 2) does not cross the x-axis, so there are no real values of x that make y=0. That means the two zeros are both complex.

Answer:

A one-tailed t statistic

Step-by-step explanation:

Answer:

x = ±(√y)/3

x = ±(√2)/3

Step-by-step explanation:

Put the given information in the given equation and solve for x:

f(x) = 2

2 = 9x^2 . . . . . use 2 in place of f(x)

2/9 = x^2 . . . . divide by 9

±√(2/9) = x . . . take the square root

x = ±(√2)/3 . . . simplify

_____

Using this as an example, we can solve f(x) = y in the same way:

y = 9x^2 . . . . use y for f(x)

y/9 = x^2 . . . divide by the coefficient of x^2

±√(y/9) = x . . . take the square root; next, simplify

x = ±(√y)/3 . . . . the equation solved for x. Note this matches the above when y=2.

Answer:

4,913 people more per sq mile.

Step-by-step explanation:

First step is to calculate the population density of both cities, then we'll be able to answer the question.

We're looking for a number of people per sq mile... so we'll divide the population by the area.

Honolulu: 348,000 people on 68.4 sq miles

DensityH = 348,000 / 68.4 =  5,088 persons/sq mile

Anchorage: 298,000 people on 1,706 sq miles

DensityA = 298,000 /1 ,706 = 175 persons/sq mile

Then we do the difference...  5,088 - 175 = 4,913 more people per sq mile.

Honolulu has approximately 4913 more people per square mile compared to Anchorage.

To find the number of more people per square mile in Honolulu compared to Anchorage, we need to calculate the population density of each city. Population density is calculated by dividing the population by the area.

For Honolulu:

Population density = population / area = 348,000 / 68.4 = 5087.72 people per square mile.

For Anchorage:

Population density = population / area = 298,000 / 1706 = 174.46 people per square mile.

To find the difference, we subtract the population density of Anchorage from the population density of Honolulu:

Difference = 5087.72 - 174.46 = 4913.26 people per square mile.

Rounding to the nearest person per square mile, there are approximately 4913 more people per square mile in Honolulu compared to Anchorage.

Answer:

  Z'(-2, 3)

Step-by-step explanation:

For 90° CW rotation, the transformation is ...

  (x, y) ⇒ (y, -x)

  Z(-3, -2) ⇒ Z'(-2, 3)

By the divergence theorem,

[tex]\displaystyle\iint_{\partial D}\vec F\cdot\mathrm d\vec S=\iiint_D(\nabla\cdot\vec F)\,\mathrm dV[/tex]

We have

[tex]\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(9z+4x)}{\partial x}+\dfrac{\partial(x-7y)}{\partial y}+\dfrac{\partial(y+9z)}{\partial z}=6[/tex]

In the integral, convert to spherical coordinates, taking

[tex]x=u\cos v\sin w[/tex]

[tex]y=u\sin v\sin w[/tex]

[tex]z=u\sin w[/tex]

so that

[tex]\mathrm dV=u^2\sin w\,\mathrm du\,\mathrm dv\,\mathrm dw[/tex]

Then the flux is

[tex]\displaystyle6\int_{w=0}^{w=\pi}\int_{v=0}^{v=2\pi}\int_{u=4}^{u=5}u^2\sin w\,\mathrm du\,\mathrm dv\,\mathrm dw=\boxed{488\pi}[/tex]

The net outward flux of the vector field F across the boundary of region D is 488[tex]\pi[/tex] and this can be determined by using the divergence theorem.

Given :

D is the region between the spheres of radius 4 and 5 centered at the origin. F = <9z+4x, x-7y, y+9z>

According to the divergence theorem:

[tex]\rm \int\int_{\delta D} \bar{F}.d\bar{S} = \int\int\int_D(\bigtriangledown.\bar{F} )dV[/tex]

Now, the expression for [tex]\rm \bigtriangledown .\bar{F}[/tex] is given by:

[tex]\rm \bigtriangledown .\bar{F}(x,y,z)=\dfrac{\delta(9z+4x)}{\delta x}+\dfrac{\delta(x-7y)}{\delta y}+\dfrac{\delta(y+9z)}{\delta z}[/tex]

Now, the spherical coordinates is given by:

x = u cosv sinw

y = u sinv sinw

z = u sinw

Therefore, the value of dV is given by:

[tex]\rm dV = u^2sinw\;du\;dv\;dw[/tex]

Now, the net outward flux of the vector field F across the boundary of region D is given by:

[tex]\rm \int\int_{\delta D} \bar{F}.d\bar{S} =\rm \int^{\pi}_0\int^{2\pi}_0\int^5_4 u^2sinw\;du\;dv\;dw[/tex]

Simplify the above integral.

[tex]\rm \int\int_{\delta D} \bar{F}.d\bar{S} =488\pi[/tex]

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Answer:

Step-by-step explanation what does it mean by how strong ?

Answer:

Step-by-step explanation:

23A:   Simplify

V^2  + 11V + 10

There are no like terms

Answer when simplify: V^2 + 11V + 10

23B.  Factor:

Steps: V^2  +  11V  + 10

Break the expression into groups:

(V^2  + V)  +  (10V   +  10)

Factor out: V From V^2  + V:   V(V  + 1)

Factor out:  10 From  10V  +  10:   10(V  +  1)

V(V  +  1)  +  10(V  +  1)

Factor out common term:  V  +  1

Factor: Therefore your Answer: (V  + 1) (V  +  10)

24:  Factor

Steps: k^2   +  11k  + 30

Break the expression into groups:

(K^2 + 5K)(6K + 30)

Factor out: k from K^2 + 5K ====>  K(K + 5)

Factor out 6  from 6K + 30 ===> 6(K + 5)

=  k(k + 5)  +  6(k  + 5)

Factor out common term: k  + 5

Factor:  Therefore your Answer is: (K + 5) (K + 6)

25:  Factor

Steps:     R^2   -   1

Rewrite:  1  as  1^2

R^2   -  1^2

Apply difference of two square formulas:

x^2   -   y^2   =   (x   +   y)(x   -  y)

r^2   -  1^2  =  (r  +  1)(r   -  1)

Therefore your answer:  (r  + 1)(r  -  1)

26:  Factor

Steps:  V^2  -  V  - 2

Break the expressions into groups:

(V^2  + V)  +   ( -2V   -  2)

Factor out V from V^2  + V:    V(V  +  1)

Factor out  -2  from  -2v   - 2:    -2(V  +  1)

V(V   +   1)   - 2(V  +  1)

Factor out common term:  V   +  1

Therefore your answer: (V  +  1)(V  -  2)

27:  Factor

Steps:  4N^2  -  15N   -  25

Break expression into groups:

(4N^2  +  5N)   +   ( -20N  -  25)

Factor out N from 4N^2  +  5N:   4(4N  +  5)

Factor out   -5   from  -20N  -  25:    -5(4N   +  5)

N(4N  +  5)  -  5(4N   +   5)

Factor out common term:  4N   +   5

Therefore your answer:   (4n  +  5)(N   -  5)

28: Factor:

Steps:   N^2   +  3N   -  54

Break the expression into group:

(N^2  -  6N)   +   (9N   -  54)

Factor out N from N^2  -  6N:    N(N   - 6)

Factor out   9  From 9N  -  54:    9(N  -  6)

N(N  -  6)    +   9(N   -   6)

Factor out common term:    N    -    6

Therefore your answer:   (N   -  6)(N   +   9)

Hope that helps, Have an awesome day!     :)

Answer:

Step-by-step explanation:

If Ð1 and Ð2 are congruent, then mÐ1 = mÐ2.

We have mÐ1 = 10x - 5 and mÐ2 = 6x + 15.

The equation:

10x - 5 = 6x + 15      add 5 to both sides

10x - 5 + 5 = 6x + 15 + 5

10x = 6x + 20      subtract 6x from both sides

10x - 6x = 6x - 6x + 20

4x = 20       divide both sides by 4

4x : 4 = 20 : 4

x = 5

Put the value of x to the expression 10x - 5:

10(5) - 5 = 50 - 5 = 45

The Pythagorean theorem says that in a right triangle the sum of the areas of the two squares on the legs equals the area of the square on the hypotenuse.

So x=

[tex] \sqrt{ {12}^{2} - {5}^{2} } [/tex]

≈10.9

Answer:

x = 10.9087121146

Step-by-step explanation:

Pythagoras theorem states a² = b² + c²

In this case a = 5, b = 12 and c = x

Therefore,

→ x² = 12² - 5²

⇒ ( Simplify )

→ x² = 144 - 25

⇒ ( Simplify )

→ x² = 119

⇒ ( Square root )

→ x = 10.9087121146

Answer:

The numbers are 38, 39, and 40

Step-by-step explanation:

Let the 3 consecutive Integral numbers be;

x, x+1, x+2

We are informed that the sum of the 3 consecutive Integral numbers is 117. Therefore;

x + x+1 + x + 2 = 117

3x + 3 = 117

3x = 114

x = 38

x+1 = 39

x+2 = 40

Answer:

38, 39, 40

Step-by-step explanation:

Here's an interesting solution to this one. The formula to compute the nth triangular number, which is to say the sum of the first n consecutive integers, starting at 1 is

[tex]\frac{n(n+1)}{2}[/tex]

What if we wanted to start from a higher number, though? Say, 3. Well, we'd have to shift every number in the sequence up 2 (1, 2, 3 would become 3, 4, 5) so we'd be adding 2 n times. If we wanted to be more general, we could call that "shift amount" s, and our modified formula would now look like

[tex]\frac{n(n+1)}{2}+sn[/tex]

Now let's put this formula to the test. We know what our sum is here: it's 117. And we know what our n is too; we're finding 3 integers, so n = 3. This gives us the equation

[tex]\frac{3(3+1)}{2} +3s=117[/tex]

Solving this equation for s:

[tex]\frac{3(4)}{2} +3s=117\\\\\frac{12}{2}+3s=117\\ 6+3s=117\\3s=111\\s=37[/tex]

so our "shift amount" is 37, and our sequence gets shifted from 1, 2, 3 to 38, 39, 40.

This was a lot of setup for what seems like a disappointing payoff, but the real power with this approach is that we've actually just solved every problem of this type. Let's say you had to find the sum of 5 consecutive integers, and their sum was 70. Not a problem. Just set our n = 5 and solve:

[tex]\frac{5(6)}{2} +5s=70\\\\\frac{30}{2} +5s = 70\\15+5s=70\\5s=55\\s=11[/tex]

Which gives us a "shift" of 11 and the sequence 12, 13, 14, 15, 16 (which is exactly the sequence I came up with for this problem!)

Answer:

  1,456

Step-by-step explanation:

The sum of n terms of a geometric sequence with first term a1 and common ratio r is given by ...

  Sn = a1·(r^n -1)/(r -1)

For your series with a1=4, r=3, and n=6, the sum is ...

  S6 = 4·(3^6 -1)/(3 -1) = 2·728 = 1,456

Explanation:

The number before the "and" or the comma is the integer portion of the number. The decimal fraction portion follows. "Tenths", or "hundredths", or "thousandths" tells you the denominator, hence the location of the rightmost digit. Otherwise the fraction digits are represented normally. ("two hundred seventy-eight" is still 278, for example.)

a. six and two tenths: 6.2

b. seventeen and four hundredths: 17.04

c. four hundred, and thirty-five thousandths: 400.035

d. fifty-six, and two hundred seventy-eight thousandth: 56.278

_____

"thirty-five thousandths" can be written as 35/1000 or 0.035. Both are pronounced the same and mean the same thing.

Step-by-step explanation:

Consider the provided information.

Mixed decimal is a number, which consisting of an integer plus a decimal.

For example:8.128 consists an integer which is 8 plus a decimal; 0.128

The Place value chart is shown in figure 1.

Part (a)

a. Six and two tenths:

Six is an integer and tenths shows the place value just after decimal.

Which can be written as:

6.2

Part (b)

Seventeen and four hundredths:

Seventeen is an integer and place 4 at hundredths place.

Which can be written as:

17.04

Part (c)

Four hundred, and thirty-five thousandths:

Four hundred is an integer and place 35 according to the place value where 5 should be at thousandths place and 3 should be hundredths place.

Which can be written as:

400.035

Part (d)

Fifty-six, and two hundred seventy-eight thousandths:

Fifty-six is an integer and place 278 according to the place value where 8 should be at thousandths place, 7 should be hundredths place and 2 should be tenths place.

Which can be written as:

56.278

Answer: Answers 2, 3, and 5

Step-by-step explanation:

In finding the volume of a prism, you can use the formula V = Bh

This happens to be one of the answers here.

Before you get to V = Bh, however, you have to find the area of the base (B).

For this you can use the are of a rectangle, or A = bh.

This is also one of the answers.

(Keep in mind that the h in the first and second equations are two different heights. The height in the volume equation refers to the height of the prism whereas the height in the area equation refers to the base's height)

Plugging in the numbers:

A = bh = 9.5 × 24 = 228

V = Bh = 228 × 6 = 1368

This is the last answer.

Answer:

1, 3, 4, 5

Step-by-step explanation:

The coefficient is the number with a variable ( letter)

In the given equation you have -2x, where x is the variable, so the coefficient would be -2.

The answer is B.

Answer:

sin F = a/c

Step-by-step explanation:

The sin ratio by definition for a given angle is the side opposite that angle over the hypotenuse.  The only thing that will never change sides in a right triangle is the hypotenuse.  In other words, no matter what angle you look at, while the side opposite one angle may be the adjacent side to a different angle, the hypotenuse is always the hypotenuse.  That means that c is the hypotenuse in our triangle.  The side opposite angle F is a, so the sin of F = a/c.

Answer:

x= 1.8

Step-by-step explanation:

We have been given the equation;

-(6)^(x-1)+5=(2/3)^(2-x)

We are required to determine the value of via graphing. To do this we can split up the right and the left hand sides of the equation to form the following two separate equations;

y = -(6)^(x-1)+5

y = (2/3)^(2-x)

We then proceed to graph the two equations on the same graph. The solution will be the point where the equations will intersect. Find the attachment below for the graph;

The value of x is 1.785. To the nearest tenth we have x = 1.8

Answer:

1.8

Step-by-step explanation:

2)  

x^2 - 14x - 32  = x^2 - 16x + 2x - 32  = x(x-16) + 2(x-16) = (x - 16)(x + 2)

---------

3)  

2n^2 - 7n - 15  =

= 2n^2 - 10n + 3n - 15 =

=  2n(n - 5) + 3(n - 5) =

= (n - 5)(2n + 3)

---------

4)  

Answer:

40 cm

Step-by-step explanation:

If we let r represent the radius of the circle, the legs of the triangle have length 5+r and 12+r. Then the Pythagorean Theorem tells us ...

(5 +12)^2 = (5 +r)^2 +(12 +r)^2

5^2 +2·5·12 +12^2 = 5^2 +2·5·r +r^2 + 12^2 +2·12·r +r^2

120 = 34r +2r^2 . . . . subtract 5^2 +12^2

60 +8.5^2 = 8.5^2 +17r +r^2 . . . . . . divide by 2, add (17/2)^2

11.5 = 8.5 +r . . . . . . . . . . . . . . . . . . . take the square root (negative root is extraneous)

3 = r

The radius of the circle is 3 cm. The perimeter of the triangle is the sum of the side lengths:

(5 +3) cm + (12 +3) cm + (5+12) cm = 2(5 +12 +3) cm = 40 cm

To find the perimeter of the right triangle, we need to find the lengths of its three sides. We can use the Pythagorean theorem to find the lengths of the legs of the triangle. The perimeter of the triangle is the sum of the lengths of all three sides.

To find the perimeter of the right triangle, we need to find the lengths of its three sides. Let's denote the lengths of the triangle's legs as a and b, and the hypotenuse as c. We are given that the point of tangency divides the hypotenuse into segments of 5 cm and 12 cm. Since the point of tangency is equidistant from the ends of the hypotenuse, the length of the hypotenuse is equal to the sum of these two segments, so c = 5 cm + 12 cm = 17 cm.

Using the Pythagorean theorem, we can find the lengths of the legs a and b. The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So we have a² + b² = c². Substituting the given values, we get a² + b² = 17 cm².

Finally, the perimeter of the triangle is the sum of the lengths of all three sides: P = a + b + c. We can solve for a and b using the equation a² + b² = 17 cm², and then calculate the perimeter.

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Answer:

D. 7.8°

Step-by-step explanation:

There are many ways to work this problem. One is to subtract the angle of V from that of W:

∠V = arctan(2/-5) ≈ 158.20°

∠W = arctan(2/-8) ≈ 165.96°

Then ∠W -∠V = 165.96° -158.20° = 7.76° ≈ 7.8°

___

Another is to divide W by V, since the quotient will have an angle that is the difference of their two angles.

(-8i +2j)/(-5i +2j) = (1/29)(44i +6j)

Then the angle of that is ...

arctan(6/44) ≈ 7.8°

___

You can also divide the dot product by the product of the two magnitudes to find the cosine of the angle between the vectors.

(V•W)/(|V|·|W|) = 44/√(68·29) = cos(x)

x = arccos(0.990830168...) ≈ 7.8°

___

A plot on graph paper will let you measure the angle with a protractor. You can obtain sufficient accuracy to choose between the offered answers.

___

Your graphing calculator may have complex number functions that let you work directly with the angles of the vectors. (See second attachment. The calculator is in degrees mode.) Doing 2-dimensional vector calculations on a calculator may best be accomplished by treating them as complex numbers.

The angle between two vectors can be found using the dot product formula. Calculate the dot product and the magnitude of each vector, substitute these values into the formula, and solve for the angle.

To find the angle between two vectors V and W, you can use the dot product formula, which states that the dot product of two vectors is equal to the magnitude of each vector multiplied by the cosine of the angle between them. In this case, the vectors are V=-5i+2j and W=-8i+2j. The dot product of V and W is (-5*-8) + (2*2) = 44. The magnitude of V is sqrt((-5)^2 + 2^2) = sqrt(29) and the magnitude of W is sqrt((-8)^2 + 2^2) = sqrt(68).

Then, we plug these values into the dot product formula: 44 = sqrt(29) * sqrt(68) * cos(theta), and solve for theta. The resulting angle, rounded to one decimal place, is the correct answer. Comparing this calculated value to the options given, we can conclude the correct answer.

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Answer:

  year 7

Step-by-step explanation:

If we assume that investment A earns interest compounded annually, its value can be modeled by the equation ...

  A = 50·(1+0.08)^(t-1) . . . . . where t is the year number

The second investment earns $3 per year, so its value can be modeled by the equation ...

  B = 60 + 3(t -1) . . . . . . . . . where t is the year number

We are interested in finding the minimum value of t such that ...

  A > B

  50·1.08^(t-1) > 60 +3(t-1)

This is a mix of exponential and polynomial terms for which no solution method is available using the tools of Algebra. A graphing calculator shows the solution to be ...

  t > 6.552

The value at the end of year 1 is found for t=1, so the values of interest are seen after 6.55 years, in year 7.

Answer:

10 in.

Step-by-step explanation:

The area of a rhombus is the product of the lengths of the diagonals divided by 2.

Let the diagonals be x and y.

area = xy/2

Here you have

area = 40 in.^2

x = 8 in.

We are looking for y, the other diagonal.

xy/2 = area

(8 in.)y/2 = 40 in.^2

(8 in.)y = 80 in.^2

y = 10 in.

Answer: The other diagonal has length 10 in.

Answer is provided in the image attached.

Answer:

Option A is the correct answer.

Step-by-step explanation:

The slope intercept form is: y=mx+b

We need to find m slope and b is the y intercept.

So, first we find the slope m of the given points.

[tex]m = \frac{y_{2} -y_{1}}{x_{2} -x_{1}} \\m= \frac{8-(-4)}{-1-(5)}\\ m= \frac{12}{-6}\\ m=-2[/tex]

After finding the slope, we can find the y intercept.

So, Option A is the correct answer.

Answer:

A

Step-by-step explanation:

The correct answer is: C. The demand for drug X shifts to the left, and the supply curve for drug X shifts to the left. The result is an unknown change in the equilibrium price for drug X and a fall in the equilibrium quantity of drug X.

Explanation:

1. The study showing that drug X is less effective than drug Y implies a decrease in the perceived effectiveness of drug X. This could lead to a decrease in the demand for drug X as consumers may prefer the more effective drug Y.

2. The increase in the price of ingredients used to produce drug X would lead to an increase in the production cost of drug X. This could cause a leftward shift in the supply curve for drug X, as producers may be less willing or able to supply the same quantity at the previous prices.

Both a decrease in demand and a leftward shift in the supply curve would result in a fall in the equilibrium quantity of drug X. The impact on the equilibrium price is uncertain and would depend on the magnitude of the shifts in demand and supply. Therefore, option C reflects these potential changes in demand and supply without making specific predictions about the equilibrium price.

The correct answer is C: The demand for drug X shifts to the left, and the supply curve for drug X shifts to the left, resulting in an unknown change in equilibrium price for drug X and a decrease in the equilibrium quantity.

The student asked about the consequences on equilibrium price and equilibrium quantity for drug X following two events: a study showing drug X is less effective than drug Y, and an increase in the price of ingredients used to produce drug X.

Analyze each event's impact on demand and supply separately: The less effective study would cause the demand for drug X to shift to the left, implying a decrease in the quantity demanded at each price because consumers now prefer drug Y. Additionally, the increase in production costs would create a supply curve shift for drug X to the left, representing a decrease in supply at each price point. When both supply and demand shift to the left, the equilibrium quantity will clearly decrease; however, the impact on the equilibrium price is uncertain without knowing the relative magnitude of the shifts.

Choosing from the provided options, answer C is correct: The demand for drug X shifts to the left, and the supply curve for drug X shifts to the left. The result is an unknown change in the equilibrium price for drug X and a fall in the equilibrium quantity of drug X.

To find the absolute maximum and absolute minimum values of the function f(x) = 6x^3 - 9x^2 - 108x + 5 on the interval [-3, 4], we can start by finding the critical points of the function and evaluating it at these points and the endpoints.

To find the absolute maximum and absolute minimum values of the function f(x) = 6x^3 - 9x^2 - 108x + 5 on the interval [-3, 4], we can start by finding the critical points of the function. These occur when the derivative of f(x) is equal to zero or undefined.

Next, we evaluate the function at these critical points as well as at the endpoints of the interval [-3, 4]. The highest value among these will be the absolute maximum value, while the lowest value will be the absolute minimum value.

After performing these steps, we find that the absolute maximum value of f(x) on the interval [-3, 4] is 59 and the absolute minimum value is -215.

-Original Profit-

y = 22x ; where x is the number of necklaces sold and y is the mount of profit.

y = 29x ; where x is the number of necklaces sold and y is the amount of profit.

Xavier will earn an additional $7 if he proceeded in switching to a new type of pendant. The $7 is the difference of $29 and $22 profit.

if x is the amount sold and y is the profit, then the original equation would be y = 22x since originally he was selling them for $22 dollars each. That means that in the equation y = 29x, 29 is the amount of profit per each necklace. From here it's just simple subtraction. New profit - Old profit = How much more earned $29 - $22 = $7 extra earned per necklace. he would save $7.