Question

Given:

1. The function f(x)=4x2+4x+6.
2. The derivative of f(x) is correctly calculated as f′(x)=4x2+4x+62(2x+1).
3. The cost function C(x)=3000+10x−0.05x2.
Objective: Find the marginal average cost function Cave′(x).

Answer 1

To find the marginal average cost function Cave′(x), we need to calculate the derivative of the cost function C(x). The function is C(x) = 3000 + 10x - 0.05x^2. The derivative is 10 - 0.1x.

Step-by-step explanation:

To find the marginal average cost function Cave′(x), we need to calculate the derivative of the cost function C(x). The cost function is given as C(x) = 3000 + 10x - 0.05x^2.

To find the derivative, we differentiate the function with respect to x. The derivative of the constant term 3000 is 0. The derivative of 10x is 10. And the derivative of -0.05x^2 is -0.1x.

Therefore, the marginal average cost function Cave′(x) is 10 - 0.1x.