Continuous differentiable?
The figure shows two parts of the graph of a continuous differentiable function

on [-10,4].
The derivative

is also continuous.
(a) Explain why

must have at least one zero in [-10,4].
(b) Explain why

must also have at least one zero in the interval [-10,4]. What are these zeros called?
(c) Make a possible sketch of the function with one zero of

on the interval [-10,4]