Hello, please help me. I just can't seem to figure this out

Suppose a total cost function is given by TC=0.01Q^{2}+5Q+100, where TC is total cost (£'s) and Q is output (units). Find the output level that minimises average total cost (ATC)

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- Aug 12th 2012, 06:09 AMJames127Application of business calculus
Hello, please help me. I just can't seem to figure this out

Suppose a total cost function is given by TC=0.01Q^{2}+5Q+100, where TC is total cost (£'s) and Q is output (units). Find the output level that minimises average total cost (ATC) - Aug 12th 2012, 06:18 AMProve ItRe: Application of business calculus
- Aug 12th 2012, 06:31 AMJames127Re: Application of business calculus
Yes, but the part that confuses me is that:

ATC = TC/Q

=0.01Q+5+100/Q

Where can you go from there with 100/Q?

Or am I confusing something that should be a lot simpler... - Aug 12th 2012, 06:33 AMProve ItRe: Application of business calculus
I assumed that the function TC given was the Average Total Cost.

If ATC = TC/Q as you believe, then write 100/Q as 100Q^(-1). You should know how to differentiate a function of the form ax^n. - Aug 12th 2012, 06:37 AMskeeterRe: Application of business calculus
total cost,

$\displaystyle C = 0.01Q^2 + 5Q + 100$

average total cost**per unit**,

$\displaystyle \bar{C} = 0.01Q + 5 + \frac{100}{Q}$

find $\displaystyle \frac{d\bar{C}}{dQ}$ , and use the first derivative test to determine the value of $\displaystyle Q$ that minimizes $\displaystyle \bar{C}$