The cost for a toy company to produce x Cosmic Starships is C(x) = 1400 + 6x − 0.01x2. What
is the marginal average cost function?
Can someone please explain how to do this to I have no idea where to start? I need to know the steps.
marginal cost function=changeinCost/unit
c'(x)=dC/dx= 6-.02x
My answer is saying it is -1400/x^2 -0.01 but I got C'(x) = 6 - 0.02x. Why is this?
To find the marginal average cost function, we need to differentiate the cost function with respect to the quantity of Cosmic Starships produced. Follow these steps:
1. Start with the given cost function: C(x) = 1400 + 6x - 0.01x^2.
2. Differentiate the cost function with respect to x using the power rule for differentiation.
3. The power rule states that if f(x) = ax^n, then the derivative of f(x) with respect to x is f'(x) = nax^(n-1).
4. Apply the power rule to each term of the cost function:
- The derivative of the constant term 1400 is zero since the derivative of a constant is zero.
- The derivative of 6x is 6, since the derivative of x is 1 and 6 is the coefficient of x.
- The derivative of -0.01x^2 is -0.02x, since the derivative of x^2 is 2x and -0.02 is the coefficient of x^2.
5. Add up the derivatives of each term to find the derivative of the entire function:
- C'(x) = 0 + 6 - 0.02x = 6 - 0.02x.
6. Simplify the derivative to get the marginal average cost function: MAC(x) = 6 - 0.02x.
Therefore, the marginal average cost function is MAC(x) = 6 - 0.02x.