What is the average rate of change between x and x + h for the function $\displaystyle f(x)=(2x+4)/x$ . Show your simplification.

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- Aug 3rd 2010, 11:53 AMilovemymathAverage Rate Of Change
What is the average rate of change between x and x + h for the function $\displaystyle f(x)=(2x+4)/x$ . Show your simplification.

- Aug 3rd 2010, 12:16 PMeumyang
$\displaystyle f(x)=\dfrac{2x+4}{x}$

Find f(x + h):

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

Plug f(x + h) and f(x) into

$\displaystyle \dfrac{f(x + h) - f(x)}{h}$

and simplify. - Aug 3rd 2010, 12:17 PMAckbeet
$\displaystyle \dfrac{f(x + h) - f(h)}{h}$ is incorrect. It should be

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

[EDIT] Typo fixed. - Aug 3rd 2010, 12:19 PMeumyang
Yes, of course. Fixed now.