Math  /  Calculus

QuestionA company determined that the marginal cost, C(x)C^{\prime}(x) of producing the xx th unit of a product is given by C(x)=x34xC^{\prime}(x)=x^{3}-4 x. Find the total cost function CC, assuming that C(x)C(x) is in dollars and that fixed costs are $8000\$ 8000.

Studdy Solution
Substitute C0=8000 C_0 = 8000 back into the expression for C(x) C(x) :
C(x)=x442x2+8000 C(x) = \frac{x^4}{4} - 2x^2 + 8000
The total cost function C(x) C(x) is:
C(x)=x442x2+8000 C(x) = \frac{x^4}{4} - 2x^2 + 8000

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