Chapter 4.5, Problem 1PQ

To determine

To sketch:

An arc where $f\text{'}\text{ and }f\text{'}\text{'}$ have sign combination $++$. Do the same for $-+$

Key concepts used:

In order to decide the sign of the first derivative, we look where the graph is increasing and where it is decreasing. The sign of $f\text{'}$ is positive when graph is increasing. The sign of $f\text{'}$ is negative when graph is decreasing.

In order to decide the sign of the double derivative, we look where the graph is concave up and where it is concave down. The sign of $f\text{'}\text{'}$ is positive when graph is concave up. The sign of $f\text{'}\text{'}$ is negative when graph is concave down.