# How do you find the average rate of change of f(x)=x^3-3x+5 over [-4,-3]?

##### 1 Answer
Nov 7, 2015

$34$

#### Explanation:

Average rate of change may be given by $m = \frac{\Delta y}{\Delta x}$

So in this case, when x changes from -4 to -3, y changes from f(-4) to f(-3).

But $f \left(- 4\right) = {\left(- 4\right)}^{3} - 3 \left(- 4\right) + 5 = - 47$

Similarly $f \left(- 3\right) = {\left(- 3\right)}^{3} - 3 \left(- 3\right) + 5 = - 13$

Thus average rate of change (average gradient or slope) between these two points is
$m = \frac{\Delta y}{\Delta x} = \frac{- 13 - \left(- 47\right)}{- 3 - \left(- 4\right)} = 34$