Question

the graph of $g$ is given below:
answer the following questions about the graph of $g$ based on the information related to $g$ and $g$.
a) state the $x$-values over which $g$ is increasing.
b) state the $x$-values over which $g$ is decreasing.
c) state the $x$-values where $g$ has horizontal tangent lines.
d) state the $x$-values over which $g$ is differentiable.

Explanation:

Step1: Recall the increasing function rule

A function \(g(x)\) is increasing when \(g^{\prime}(x)>0\).

Step2: Analyze the graph of \(g^{\prime}(x)\)

Looking at the graph of \(y = g^{\prime}(x)\), we find the intervals where the graph is above the \(x -\)axis.
From the graph, \(g^{\prime}(x)>0\) on the intervals \((-\infty,- 6)\cup(-4,3)\cup(7,\infty)\)

Answer:

\((-\infty,-6)\cup(-4,3)\cup(7,\infty)\)