Originally Posted by

**MarkFL2** We have the two roots of the first derivative as critical numbers $\displaystyle x=0,\,2$.

So, using the second derivative $\displaystyle f''(x)=6(x-1)$ we evaluate this second derivative at the critical numbers:

*i*) $\displaystyle f''(0)=6(0-1)=-6$

Now, since this is less than zero, we know we have a relative maximum at:

$\displaystyle (0,f(0))=(0,3)$

*ii*) $\displaystyle f''(2)=6(2-1)=6$

Now, since this is greater than zero, we know we have a relative minimum at:

$\displaystyle (2,f(2))=(2,-1)$