Question

Find the cost function for the following marginal cost function, given that the fixed cost is $10

c'(x)=0.6x² +4x

Answer 1

To find the cost function, integrate the given marginal cost function and find the value of the constant of integration using the provided fixed cost. The cost function is 0.2x³ + 2x² + 10.

Step-by-step explanation:

To find the cost function, we need to integrate the given marginal cost function. The fixed cost is $10. Integrating the given marginal cost function, we get:
Cost function = ∫ (0.6x² + 4x) dx
= 0.2x³ + 2x² + C
where C is the constant of integration.
Since the fixed cost is $10, we can find the value of C by substituting the given fixed cost into the cost function:
10 = 0.2(0)³ + 2(0)² + C
10 = C
Therefore, the cost function is:
Cost function = 0.2x³ + 2x² + 10