The figure shows two parts of the graph of a continuous differentiable function f on [−10, 4]. The derivative f′ is also continuous. To print an enlarged copy of the graph, go to MathGraphs.com.

(a) Explain why f must have at least one zero in [−10, 4].

(b) Explain why f′ 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, where f′ has one zero on the interval [−10, 4].

Transcribed Image Text:

-8 -4 8 4 -4 y -8 + -Х