# How do use the first derivative test to determine the local extrema #f(x) = x³+3x²-9x+15#?

##### 1 Answer

Aug 9, 2015

#### Explanation:

First we look for points that might be the extrema by solving

Now, we can use the graph of the first derivative to determine whether those points are extrema and which type of extrema:

if when passing through point

and if from negative to positive - a locac minimum.

graph{3(x+3)(x-1) [-10, 10, -5.21, 5.21]}

In this case