Chapter 5.3, Problem 56E

To determine

To justify: whether the statement is true or false

Answer to Problem 56E

The statement is true.

Explanation of Solution

Given information: if $f\text{'}\text{'}(c)=0$ and $f\text{'}\text{'}\left(c\right)<0$ , then $f\left(c\right)$ is a local maximum.

If $f\text{'}\text{'}(c)=0$ , then f has horizontal tangent line at $x=c$ , also, if $f\text{'}\text{'}\left(c\right)<0$ , then f is concave down at $x=c$ .

Therefore, $f\text{'}\text{'}(c)=0$ is a relative extremum, then $x=c$ is a relative maximum.

Hence, the statement is true.