# Average Rate Of Change

#### ilovemymath

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

#### eumyang

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

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.

Last edited:
ilovemymath

#### Ackbeet

MHF Hall of Honor
$$\displaystyle \dfrac{f(x + h) - f(h)}{h}$$ 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.

Last edited:
ilovemymath

#### eumyang

Yes, of course. Fixed now.