# average rate of change - evaluating functions

• January 26th 2011, 01:59 PM
epimetheus
average rate of change - evaluating functions
How do you do problems such as this?

Evaluate $\frac{f(x) - f(2)}{x - 2}$ for $f(x) =$ $\frac{4}{x}$
• January 26th 2011, 02:28 PM
Aryth
Plug and chug:

$\frac{\frac{4}{x} - 2}{x - 2} = \frac{\frac{4 - 2x}{x}}{x-2} = \frac{\frac{2(2 - x)}{x}}{x-2} = \frac{-2}{x}$
• January 26th 2011, 02:43 PM
epimetheus
Is it the same thing when you have something like $\frac{f(3 + h) - f(3)}{h}$ for x² - 4?
• January 26th 2011, 02:50 PM
Aryth
Yes, it's exactly the same:

$\frac{(3 + h)^2 - 4 - (9 - 4)}{h} = \frac{9 + 6h + h^2 - 4 - 9 + 4}{h} = \frac{6h + h^2}{h} = 6 + h$