find the location of the absolute maximum and absolute minimum of the function on the interval -1,1.

Explanation:

Step1: Identify critical points

Find where $h'(x)=0$ or is undefined in $(- 1,1)$. From the graph, we look for where the slope is zero.

Step2: Evaluate function at critical and end - points

Evaluate $h(x)$ at critical points in $(-1,1)$ and at $x = - 1,x = 1$. From the graph, at $x=-1$, $h(-1)$ is some value, at critical point in $(-1,1)$ (where slope is 0) $h(x)$ has a local maximum and local minimum, at $x = 1$, $h(1)$ is some value.

Step3: Compare function values

Compare the values of $h(x)$ obtained in Step 2. The largest value is the absolute maximum and the smallest is the absolute minimum. From the graph, the absolute maximum occurs at the critical point in $(-1,1)$ where the function has a local maximum and the absolute minimum occurs at the critical point in $(-1,1)$ where the function has a local minimum.

Answer:

The absolute maximum occurs at the critical point in $(-1,1)$ where the function has a local maximum. The absolute minimum occurs at the critical point in $(-1,1)$ where the function has a local minimum.