Answer
(a) This is the graph of a function on $[-1,2]$. There is an absolute maximum at $x=2$, but there is no local maximum.
(b) This is the graph of a function on $[-1,2]$. There is a local maximum at $x=0$, but there is no absolute maximum.
Work Step by Step
(a) This is the graph of a function on $[-1,2]$. There is an absolute maximum at $x=2$, but there is no local maximum. Note that the point at $x=2$ is not a local maximum because it is an endpoint of the interval.
(b) This is the graph of a function on $[-1,2]$. There is a local maximum at $x=0$, but there is no absolute maximum.