# How do you find all local maximum and minimum points using the second derivative test given #y=x^3-9x^2+24x#?

##### 1 Answer

Mar 16, 2017

We have a local maximum at

We have a local minimum at

#### Explanation:

Let's calculate the first derivative

Let

The critical points are when

That is, when

Now, we calculate the second derivative

f''(x)=(d^2y)/dx^2=6x-18#

When

Now,

We calculate

As,

As,

graph{x^3-9x^2+24x [-36.67, 45.55, -6.95, 34.14]}