Give a brief reason why a function that is continuous on

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Give a brief reason why a function that is continuous on [a,b][a,b], differentiable on (a,b)(a,b), and satisfies f(a)=f(b)f(a)=f(b) must have at least one number cc in (a,b)(a,b) for which f′(c)=0f'(c)=0.

Related theory

Browse the problem library