Question

1. Show that f(x) = 2 Satisfy the condition of the Mean Value Theorem on [-1 , 2]. Then find numbers c given by mean value theorem.

Detailed steps are always appreciated.
Thank you : )

Answer 1

f is a horizontal line so that satisfies f is continuous and differentiable (everywhere).
f'(x) = 0
(f(2) - f(-1))/(2 - -1) = 0. so f'(c) = 0. therefore there are infinitely many c's in [-1, 2] such that f'(c) = 0.