Final answer:
To find the marginal cost when x = 8, calculate the derivative of the cost function C(x) and plug in the value x = 8 into the derivative function. Option d. 375 is the correct answer.
Step-by-step explanation:
To find the marginal cost when x = 8, we need to calculate the derivative of the cost function C(x) with respect to x. The derivative will give us the rate at which the cost is changing with respect to the quantity produced.
Given the cost function C(x) = 110+7x-x²+2x³, we can calculate its derivative as follows:
C'(x) = 0+7-2x+6x²
Now, plug in the value x = 8 into the derivative function:
C'(8) = 0+7-2(8)+6(8²) = 0+7-16+384 = 375
Therefore, the marginal cost when x = 8 is 375 (option d).