Chapter 4, Problem 22RE

Determine whether the statement is true or false. If it is false, give an example for which the statement fails.

(a) If $f$ has a relative maximum at $x_0,$ then $f\left(x_0\right)$ is the largest value that $f\left(x\right)$ can have.

(b) If the largest value for $f$ on the interval $\left(a,b\right)$ is at $x_0,$ then $f$ has a relative maximum at $x_0$ .

(c) A function $f$ has a relative extremum at each of its critical points.