# Question #cbfb8

##### 1 Answer

There is one critical number, at

#### Explanation:

Start by finding the derivative by the power rule.

#f'(x) = 3x^2 - 6x + 3#

The critical points will occur when the derivative equals

#0 = 3x^2 - 6x + 3#

#0 = 3(x^2 - 2x + 1)#

#0 = (x -1)(x - 1)#

#x = 1#

Next, we must verify whether this is a *local minimum* or a *local maximum*. Note that this function will never have an absolute maximum/minimum, as shows the table below.

We can verify whether this point is a local min or a local max by finding the intervals of increase/decrease.

**Test point 1: #x = 0#**

#f'(0) = 3(0)^2 - 6(0) + 3 = 3#

**Test point 2: #x = 3#**

#f'(3) = 3(3)^2 - 6(3) + 3 = 27 - 18 + 3 = 12#

Since

Hopefully this helps!