Chapter 4 - Section 4.1 - Maximum and Minimum Values - 4.1 Exercises - Page 283: 12

(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.

(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.