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wolverine [178]
3 years ago
7

A company determined that the marginal​ cost, C' (x )of producing the xth unit of a product is given by C' (x )= x^3- 6x. Find t

he total cost function​ C, assuming that​ C(x) is in dollars and that fixed costs are ​$3000.
Mathematics
1 answer:
Rashid [163]3 years ago
3 0

Answer:

C(x) = \frac{x^4}{4}-3x^2+3,000

Step-by-step explanation:

The marginal cost function, C'(x), is the derivate of the cost function, C(x).

Therefore, we can obtain the cost function by finding the integral of the marginal cost function:

C(x) = \int\ {C'(x)} \, dx \\C(x) = \int\ {(x^3-6x)} \, dx \\C(x) = \frac{1}{4} x^4-3x^2+a

Where 'a' is a constant and represents fixed costs. If fixed costs are $3,000, the cost function is:

C(x) = \frac{x^4}{4}-3x^2+3,000

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I’d appreciate help ASAP please and thank you!
White raven [17]
<h3>Answer:  Choice C) 40 </h3>

==========================================================

Work Shown:

Plug in x = 0

g(x) = 3^{2x}\\\\g(0) = 3^{2*0}\\\\g(0) = 3^{0}\\\\g(0) = 1\\\\

This indicates that (0,1) is on the curve. This is the y intercept.

Do the same for x = 2

g(x) = 3^{2x}\\\\g(2) = 3^{2*2}\\\\g(2) = 3^{4}\\\\g(2) = 81\\\\

So we know that (2,81) is another point on this curve.

We need to find the slope of the line through (0,1) and (2,81) to get the slope of the secant line we want.

m = \text{slope}\\\\m = \frac{\text{rise}}{\text{run}}\\\\m = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{g(2)-g(0)}{2-0}\\\\m = \frac{81-1}{2-0}\\\\m = \frac{80}{2}\\\\m = 40\\\\

The slope of the line through (0,1) and (2,81) is m = 40. This value of m is exactly the slope of the secant line your teacher is asking for. This is why the answer is choice C.

5 0
2 years ago
Will give brainless if solved
wel

Answer:

1. 70  2. 85  3. 63  4. 20  5. They are vertical angles

Step-by-step explanation:

6 0
3 years ago
11. An ice-cream cone and it's dimensions are shown in the diagram.
Mashutka [201]

Answer:

i donnt know sorry

Step-by-step explanation:

3 0
2 years ago
What is the conclusion of the statement in the box below?
Nady [450]

Answer:

D

Step-by-step explanation:

x²=4

x=√4

X1=2

X2=-2

6 0
2 years ago
Twenty-one fish are swimming in an aquarium. Eleven are removed, leaving 10 fish. Which number is the additive inverse of the nu
agasfer [191]

The additive inverse: The usage of addition with a negative number.

The original equation is 21 - 11 = 10

To use the additive inverse, change it so that there is an addition sign.

21 + (-11) = 10

B) -11 is your answer

hope this helps

7 0
2 years ago
Read 2 more answers
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