Please help me with this differential calculus question?

If the total cost (in £s) function is given by

TC = 2Q^{2} + 158Q - 12000

where Q is the quantity produced

(a) What Q would minimise total costs?

**Give your answer to 2 decimal places. **

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

**Give your answer to the nearest**

pound.

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

Re: Please help me with this differential calculus question?

Set the derivative to zero to find critical points

$\displaystyle \frac{d(TC)}{dQ} = 4Q + 158 = 0$...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).

Re: Please help me with this differential calculus question?

thanks very much for the reply, its not 4Q though it's 2Q^2, I'm confused about what the answer is, will you please help me?

Re: Please help me with this differential calculus question?

Quote:

Originally Posted by

**Ceidon** thanks very much for the reply, its not 4Q though it's 2Q^2, I'm confused about what the answer is, will you please help me?

Umm, what's the derivative of $\displaystyle 2Q^2$ with respect to Q?

Re: Please help me with this differential calculus question?

Is the answer 0 for part A? Will you please help me with part B as well?

Re: Please help me with this differential calculus question?

Quote:

Originally Posted by

**richard1234** Umm, what's the derivative of $\displaystyle 2Q^2$ with respect to Q?

Sorry I got the question wrong it's

TC = 2Q^2 - 158Q + 12000

Re: Please help me with this differential calculus question?

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

http://mathhelpforum.com/calculus/20...-question.html

also, this is not a problem in differential equations.

Re: Please help me with this differential calculus question?

Quote:

Originally Posted by

**Ceidon** Sorry I got the question wrong it's

TC = 2Q^2 - 158Q + 12000

See, this is why you should always double-check what you post...