# Rolle's theorem

• Apr 24th 2007, 11:19 AM
luckyc1423
Rolle's theorem
Rolle's theorem requires three conditions be satisfied:
i. f is continuous on [a,b]
ii. f is differentiable on (a,b), and
iii. f(a)=f(b)

Find three functions that satisfy exactly two of these three conditions, but for which the conclusion of Rolle's theorem does not follow. That is, there is no point c element of (a,b) such that f](c) = o
• Apr 24th 2007, 11:36 AM
ThePerfectHacker
Quote:

Originally Posted by luckyc1423
Rolle's theorem requires three conditions be satisfied:
i. f is continuous on [a,b]
ii. f is differentiable on (a,b), and
iii. f(a)=f(b)

Find three functions that satisfy exactly two of these three conditions, but for which the conclusion of Rolle's theorem does not follow. That is, there is no point c element of (a,b) such that f](c) = o

f(x)=|x| on [-1,1]
• Apr 24th 2007, 01:21 PM
CaptainBlack
Quote:

Originally Posted by ThePerfectHacker
f(x)=|x| on [-1,1]

violates condition ii, but satisfies the other two.

f(x) = x on [0,1]

satisfies conditions i and ii, but not condition iii.