(a) Suppose that the function giving the marginal cost, in dollars per gallon, when x gallons...

Question

Question

(a) Suppose that the function giving the marginal cost, in dollars per gallon, when x gallons oil are made is

(eq. 1) and the fixed cost (giving the cost when no barrels of oil are made) is $80. Find a function that would give the total cost, C (x), in dollars when x gallons of oil are made in the form C (x)aoa1 a2xa3 3. = (eq. 2)

What is the value for the coefficient LaTeX: a_0 ? (Hint: You may take the derivative of (eq. 2) term by term, and then equate the coefficients of like terms in this expression for C (x)
and the expression given in (eq. 1).)

(Note: This problem is not asking you to find the derivative of the marginal cost function M (x). It is asking you to find a function whose derivative is M (x)

The resulting function C (x) can be called an "antiderivative" or a "primitive" or an "indefinite integral" of $LaTeX: M\left(x\right)$ . This is not required for this course, but a notation that can be used is C (r) JM (x) da.

The dx reminds us that derivatives with respect to x are involved)..

(b) In the expression C (r) aa1xaz2 a3 3,

what is the value for the coefficient

(c) In the expression 2 C (r) aa1xaa a3 a3,

what is the value of the coefficient a2?

(d) In the expression 2 C (r) aa1xaa a3 a3,

what is the value of the coefficient

(e) Use the cost function C (x)

to determine the cost $LaTeX: C\left(2\right)$ if 2 barrels of oil are made, in dollars. (Just type a numerical answer, accurate to two decimal places).

M (x) C (x) = 50 20x +0.09x2
C (x)aoa1 a2xa3 3. =

C' (x)
M (x)
C (x)

C (r) JM (x) da.
C (r) aa1xaz2 a3 3,
ai
2 C (r) aa1xaa a3 a3,
a2?

аз

math Advanced-Math

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Answer 1

Answer #1

2 NC2)- C С») 3 50+ 201tOc0g а Сс113 с Со) 3 3о mол gven uhen С ся1Е g0+ a,taz( aъ taking Нetя lerivatve cс0- о+аft 2022tза3

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Answer 2

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