Rolle's theorem requires three conditions be satisfied:
i. f is continuous on [a,b]
ii. f is differentiable on (a,b), and
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]
Originally Posted by luckyc1423
violates condition ii, but satisfies the other two.
Originally Posted by ThePerfectHacker
f(x) = x on [0,1]
satisfies conditions i and ii, but not condition iii.