Question

The total cost, in dollars, to produce x DVD players is C(x)=130+6x−x²+5x3. Find the marginal cost when x=4.

A) $238
B) $458
C) $368
D) $328

Answer 1

To find the marginal cost for producing 4 DVD players, we calculate the derivative of the cost function and evaluate it at x=4, which results in a marginal cost of $238.

Step-by-step explanation:

The marginal cost when x equals 4 for the function C(x) = 130 + 6x - x² + 5x³ can be found by taking the derivative of C(x) and evaluating it at x = 4. The derivative, C'(x), represents the marginal cost, which is the cost of producing one more unit at a certain level of production.

To find C'(x), we differentiate each term of C(x) with respect to x:

• Derivative of 130 is 0 (constant term).
• Derivative of 6x is 6.
• Derivative of -x² is -2x.
• Derivative of 5x³ is 15x².

Therefore, C'(x) = 6 - 2x + 15x². Now substitute x = 4 into C'(x) to find the marginal cost:

C'(4) = 6 - 2(4) + 15(4)² = 6 - 8 + 15(16) = -2 + 240 = 238 dollars.

So, the marginal cost when x = 4 is $238, which corresponds to option A.