Answer
$a.$
Left endpoint is $(0,0)$ - not an absolute maximum.
The absolute maximum is at right endpoint, $(1,4.7)$
An absolute minimum is at $(0.4398,-1.061)$
$b.$
Absolute minimum: $(0.4398,-1.0613072)$
Work Step by Step
$a.$
Graphing with desmos.com (upper image),
the zeros and extrema are highlighted.
We approximate:
Left endpoint is $(0,0)$ - not an absolute maximum.
The absolute maximum is at right endpoint, $(1,4.7)$
An absolute minimum is at $(0.4398,-1.061)$
$b.$
Graphing the equation $\quad f'(x)=0$, we find a critical point at
$x\approx 0.4398$
Evaluating $f(x)$ at the endpoints and the critical point,
(see lower image)
we have a more precise value for the absolute minimum.
Absolute minimum: $(0.4398,-1.0613072)$
