# How do you locate the critical point, and determine the maxima and minima of #y=x^3-6x^2+9x-8#?

##### 1 Answer

**Critical points:**

For this function, the domain is

So the critical points for this

at

These are the critical points for this

**Testing the critical points for extrema**

You may test critical points using either the first or the second derivative test for local extrema. (A.k.a relative extrema).

Using the first derivative test (for local extrema) we look at the intervals defined by the critical points and test for

You can choose any test numbers you like, I'll choose here.

Intervals Test numbers and sign of

Arithmetic:

It's not needed to answer the question, but here is the graph:

graph{y=x^3-6x^2+9x-8 [-10.45, 21.6, -14.22, 1.8]}