Average Rate of Change

• July 13th 2010, 08:41 AM
bobsanchez
Average Rate of Change
A company that makes wooden toys has determined that the cost of producing toys is given by the function C(x) =x^2 + 7. Find the average rate of change in cost for increasing production from x =1 units to x = 4 units.

I thought I knew how to do these but I consistently get this problem wrong. Where do I start with it?
• July 13th 2010, 08:57 AM
1005
Rate of change is defined by a derivative. In calculus, the average is defined by:
$\frac{1}{T_2 - T_1} \int\limits_{T_1}^{T_2} f(x)\, dx$

To sum, you need to find:
$\frac{1}{T_2 - T_1} \int\limits_{T_1}^{T_2} f'(x)\, dx=\frac{f(T_2)-f(T_1)}{T_2-T_1}$
• July 13th 2010, 10:35 AM
bobsanchez
Ahhh okay. So the answer should be 5, correct?
• July 13th 2010, 01:59 PM
1005
Quote:

Originally Posted by bobsanchez
Ahhh okay. So the answer should be 5, correct?

That's what I calculated.