Answer
Absolute maximum $f(-1)=1$ and the absolute minimum $f(-2)=1/2$. See graph.
Work Step by Step
Step 1. Given the function $f(x)=-\frac{1}{x}, -2\leq x\leq-1$, we have $f(-2)=1/2, f(-1)=1$,
Step 2. $f'(x)=\frac{1}{x^2}\ne0$; no extrema here.
Step 3. We can identify the absolute maximum as $f(-1)=1$ and the absolute minimum as $f(-2)=1/2$ on the given interval.
Step 4. See graph.