Rolle's Theorem

Question

let f be continuous on [a;b] and differentiable on
(a;b). If there exists c in (a; b) such that f(c) = 0, is it possible for f(a) to not equal f(b)?

 

 

Answer 1

Yes.  For example, let f(x) = x².  Let a = -2, b = 1.  Then f(x) is continuous on [-2,1] and is differentiable on (-2,1).  f(-2)≠f(1), c = 0 is in the interval (-2,1) and f(c)=0.