Question

Hello! I'm stuck on this problem of my homework (Calculus student in highschool here) and wanted to see if someone could help? I would appreciate a clarification on what exactly makes "h" NOT differentiable (according to the graph included)

Answer 1

We are given a graph of a function h(x) and asked to find out if there are any points where the function is not differentiable.

Recall that a function is not differentiable at points where there exists a discontinuity.

Notice that at x = -4 the function is discontinuous.

So, x = -4 is one of the x-values for which h(x) is NOT differentiable.

Also, notice that the function h(x) has a vertical asymptote at x = -5

Since there is an asymptote at x = -5, the limit at this point is undefined and hence the function is NOT differentiable.

Therefore, x = -4 and x = -5 are two values for which h(x) is NOT differentiable.