(c) The derivative of a function at a given point is the slope of the tangent line at that point. So, if you can’t draw a tangent line, there’s no derivative.
From the graph, we can determine the values of x that f'(x) is undefined to be:
Answer: -3, -1, 3, 5
(d) The derivative of a function is zero when there is a horizontal tangent at that point.
From the graph, we can determine the values of x where f'(x) is zero to be:
Answer: 0, 2