Consider the function f(x)={-2x,x<=1 2x-4,x>1. Note that f(0)=f(2)=0. Your friend claims that by the Mean Value Theorem, f'(c) should be zero for some c with 0<c<2.

Question

a. Find such a value of c or show that it does not exist

b. Does your answer to part a) contradict the Mean Value Theorem? Give reasons for your answer

Answer 1

Hi Robert,

I hope this helps to answer your question and gives you a better understand of the MVT in general! It's definitely a hard topic -- good luck!

Ross