Cost derivative + finding x value

[Ric]

[Solved]Cost derivative + finding x value

I believe I'm supposed to make C'(x)=0 to find a minimum but I can't figure out how to factor the derivative of C(x) to solve for possible "x"s. Or is there another way to do this?

Edit: C(x)= total cost.

 

[daon2]

I believe I'm supposed to make C'(x)=0 to find a minimum but I can't figure out how to factor the derivative of C(x) to solve for possible "x"s. Or is there another way to do this?

It says to minimize marginal cost, not cost. Set C''(x) = 0

 

[Ric]

There is no economic reason to minimize marginal cost...the problem should also call C(x) total cost to clarify the nature of the problem.

It is as the textbook asks; "minimize marginal cost". C(x)= total cost. How does the double derivative of "total cost" minimize marginal cost?

 

[pka]

How does the double derivative of "total cost" minimize marginal cost?

The first derivative of \(\displaystyle C(c)\) gives marginal cost.
Thus to minimize marginal cost,we look that the derivative of marginal cost.
That is the second derivative of \(\displaystyle C(x)\).

BTW: Here is theorem in economics.
Minimum average cost occurs there average cost equals marginal cost.