Question

identify all of the values of c for which h(c) = 0. if there is more than one value, enter the values as a comma - separated list. if there are none, enter dne. values: identify all of the values of c for which h(c) does not exist. if there is more than one value, enter the values as a comma - separated list. if there are none, enter dne. values:

Explanation:

Step1: Recall derivative - zero condition

The derivative $h^{\prime}(c)=0$ at horizontal tangent points.

Step2: Identify horizontal - tangent $x$ - values

From the graph, the function $y = h(x)$ has a horizontal tangent at $x = 1$. So for $h^{\prime}(c)=0$, $c = 1$.

Step3: Recall non - differentiable conditions

The derivative $h^{\prime}(c)$ does not exist at sharp corners and vertical tangents.

Step4: Identify non - differentiable $x$ - values

The function $y=h(x)$ has sharp corners at $x=-2$ and $x = 0$. So for $h^{\prime}(c)$ not existing, $c=-2,0$.

Answer:

For $h^{\prime}(c)=0$, values: $1$
For $h^{\prime}(c)$ does not exist, values: $-2,0$