Chapter 13.3, Problem 35E

To determine

To estimate : Arrange the given number sin increasing order and explain your reasoning.

Answer to Problem 35E

The numbers in increasing orders are $g\text{'}\left(0\right)<0<g\text{'}\left(4\right)<g\text{'}\left(2\right)<g\text{'}\left(-2\right)$.

Explanation of Solution

Given information:

The graph g is given and the numbers are 0, $g\text{'}\left(-2\right)$ , $g\text{'}\left(0\right)$ , $g\text{'}\left(2\right)$ and $g\text{'}\left(4\right)$.

Calculation :

The derivative of the graph at point $a$ is the slope of the tangent to the graph at $x=a$.

It can be observed the slope at $x=0$ is negative. Therefore, $g\text{'}\left(0\right)<0$.

The slope at $x=4$ is smaller than the slope at $x=2$ and both are smaller than the slope at $x=-2$.

Hence,

The numbers in increasing orders are $g\text{'}\left(0\right)<0<g\text{'}\left(4\right)<g\text{'}\left(2\right)<g\text{'}\left(-2\right)$.