# Average Rate Of Change

• August 3rd 2010, 11:53 AM
ilovemymath
Average Rate Of Change
What is the average rate of change between x and x + h for the function $f(x)=(2x+4)/x$ . Show your simplification.
• August 3rd 2010, 12:16 PM
eumyang
$f(x)=\dfrac{2x+4}{x}$

Find f(x + h):
$f(x)=\dfrac{2(x+h)+4}{x+h} = \ldots$

Plug f(x + h) and f(x) into
$\dfrac{f(x + h) - f(x)}{h}$
and simplify.
• August 3rd 2010, 12:17 PM
Ackbeet
$\dfrac{f(x + h) - f(h)}{h}$ is incorrect. It should be

$\dfrac{f(x + h) - f(x)}{h}.$ That's the slope of the secant line, which also happens to be equal to the average rate of change.

[EDIT] Typo fixed.
• August 3rd 2010, 12:19 PM
eumyang
Yes, of course. Fixed now.