Answer
$(-0.8, -5.9104) \quad$ local minimum
$(0.2541,2.504) \quad$ local maximum
$(1.8608, -6.268)$ $\quad$ absolute minimum
$(2.56, 2.7609) \quad$ absolute maximum
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).
$(a)$
$Enter$:$\quad f(x):=x^{4}-8x^{2}+4x+2$
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 $-20/25$ and $64/25$.
(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.
$(c)$
$f'(x)$ is a polynomial, defined everywhere.
If you want to plot it, 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, $-0.8$
critical values $0,2541, 1.8608$
the right endpoint, $2.56$.
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.
$(e)$
$(-0.8, -5.9104) \quad$ local minimum
$(0.2541,2.504) \quad$ local maximum
$(1.8608, -6.268)$ $\quad$ absolute minimum
$(2.56, 2.7609) \quad$ absolute maximum
