Answer
$f(x)$ has an absolute maximum value of $0$ at $x=-4$ and an absolute minimum value of $-5$ at $x=1$.
Work Step by Step
$$f(x)=-x-4\hspace{1cm}-4\le x\le1$$
1) Find the derivative $f'(x)$: $$f'(x)=-1$$
Since the value of $f'(x)$ is constant and equals $-1$, $f(x)$ has no critical points.
2) Evaluate $f(x)$ at the endpoints:
- For $x=-4$: $$f(-4)=-(-4)-4=4-4=0$$
- For $x=1$: $$f(1)=-1-4=-5$$
This means the function $f(x)$ has an absolute maximum value of $0$ at $x=-4$ and an absolute minimum value of $-5$ at $x=1$.
