Answer
The absolute maximum $f(0)=2$ and the absolute minimum $f(3)=-1$ on the given interval.
See graph.
Work Step by Step
Step 1. Given the function $f(t)=2-|t|, -1\leq t\leq 3$, we have $f(-1)=1, f(3)=-1$,
Step 2. Consider a possible critical point at $x=0$, we have $f(0)=2$
Step 3. We can identify the absolute maximum $f(0)=2$ and the absolute minimum $f(3)=-1$ on the given interval.
Step 4. See graph.