Answer
$(-2, 7.937) \quad$ absolute maximum
$(0, 0 )$ $\quad$ absolute minimum
$(1.2 2.0326$) $\quad$ local maximum
$(2,1.5874) \quad$ local minimum
Work Step by Step
CAS used: geogebra.org/classic.
Set view windows: Graphics, Algebra, Spreadsheet.
Set rounding to 4 decimal places (or, as you like).
$(a)$
$Enter$:$\quad f(x):=x^{2/3}(3-x)$
Turn off the graph for f, as we will restrict its domain.
$Enter$:$\quad (x,f(x))$
The entry is modified with two parameters: the interval borders for x.
Change them to $-2$ and $2.$
(this is now labeled as a: Curve(....) )
$(b)$
$Enter$:$\quad Solve(f'(x)=0)$
This returns a list of values where the derivative is 0. Some values may be outside our restricted domain, so we will ignore those.
$(c)$
$Enter$:$\quad f1=f'(x)$
We see x in the denominator. $x=0$ is a critical value.
If you want to plot $f'$, enter $(x, f'(x))$ and adjust the interval borders.
$(d)$
In the spreadsheet window,
in column A, enter the x-coordinates of
the left endpoint, $-2$
critical values $0,1.2$
the right endpoint, $2$
In cell B1 $Enter$:$\quad =f(A1)$
and copy-paste down.
Select the values of the coordinates in the spreadsheet and "Create a list of points"
They have been added to the graph.
$(e)$
$(-2, 7.937) \quad$ absolute maximum
$(0, 0 )$ $\quad$ absolute minimum
$(1.2 2.0326$) $\quad$ local maximum
$(2,1.5874) \quad$ local minimum