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

M ( x ) = C ( x ) = 50 + 20 x + 0.09 x 2 (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 ) = a 0 + a 1 x + a 2 x 2 + a 3 x 3 .(eq. 2)

What is the value for the coefficient 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 M ( x ). This is not required for this course, but a notation that can be used is C ( x ) = M ( x ) d x .

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

Flag this Question

Question 271 pts

6 (b) In the expression C ( x ) = a 0 + a 1 x + a 2 x 2 + a 3 x 3 ,

what is the value for the coefficient a 1 ?

Flag this Question

Question 281 pts

6 (c) In the expression C ( x ) = a 0 + a 1 x + a 2 x 2 + a 3 x 3 ,

what is the value of the coefficient a 2 ?

Flag this Question

Question 291 pts

6 (d) In the expression C ( x ) = a 0 + a 1 x + a 2 x 2 + a 3 x 3 ,

what is the value of the coefficient a 3 ?

Flag this Question

Question 301 pts

6 (e) Use the cost function C ( x )

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

Transcribed image text