If the total cost (in £s) function is given by
TC = 2Q2 + 158Q - 12000

where Q is the quantity produced

(a) What Q would minimise total costs?

(b) Use your value in (a) to find the minimum value for total costs.
pound.

Please show me how to get the answer. I would be extremely grateful. Thank you.

Set the derivative to zero to find critical points

$\frac{d(TC)}{dQ} = 4Q + 158 = 0$...this only makes sense if we can produce a negative amount. If we restrict Q to non-negative numbers, then Q = 0 minimizes cost, which turns out to be negative £12000. (also doesn't make much sense).

Originally Posted by Ceidon
Umm, what's the derivative of $2Q^2$ with respect to Q?

Originally Posted by richard1234
Umm, what's the derivative of $2Q^2$ with respect to Q?

Sorry I got the question wrong it's

TC = 2Q^2 - 158Q + 12000

please do not post the same problem twice in different forums.