Answer
The absolute maximum $ f(7)=2$ and the absolute minimum $f(5)=0$ on the given interval.
See graph.
Work Step by Step
Step 1. Given the function $f(t)=|t-5|, 4\leq t\leq 7$, we have $f(4)=1, f(7)=2$,
Step 2. Considering a possible critical point at $x=5$, we have $f(5)=0$
Step 3. We can identify the absolute maximum $ f(7)=2$ and the absolute minimum $f(5)=0$ on the given interval.
Step 4. See graph.