Answer
$(0, 1) \quad$ local minimum
$(0.6619, 1.6024) \quad$ local maximum
$(2.8404, 0.7304) \quad$ absolute minimum
$(6.2832, 3.5066)$ $\quad$ 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).
$(a)$
$Enter$:$\quad f(x):=\sqrt{x}+\cos x$
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(....) )
$(b)$
Plot $f'$, and adjust the interval borders:
$Enter$:$\quad g:(x,f'(x))$
$Enter$:$\quad Intersect (g,y=0)$
This returns a list of values where the derivative is 0.
$(c)$
$Enter$:$\quad f1=f'(x)$
We see x in the denominator. $x=0$ is a critical value.
$(d)$
In the spreadsheet window,
in column A, enter the x-coordinates of
the left endpoint, $0$
critical values $0.6619,2.8404$
the right endpoint, $ 2\pi$.
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.
$(e)$
$(0, 1) \quad$ local minimum
$(0.6619, 1.6024) \quad$ local maximum
$(2.8404, 0.7304) \quad$ absolute minimum
$(6.2832, 3.5066)$ $\quad$ absolute maximum