THEOREM 4.4 Rolle's Theorem Let f be a continuous function over the closed interval [a, b] and differentiable over the o

[answerhappygod]

Theorem 4 4 Rolle S Theorem Let F Be A Continuous Function Over The Closed Interval A B And Differentiable Over The O 1 (39.96 KiB) Viewed 11 times

THEOREM 4.4 Rolle's Theorem Let f be a continuous function over the closed interval [a, b] and differentiable over the open interval (a, b) such that f(a) f(b). There then exists at least one c E (a, b) such that f'(c) = 0. In each of the following graphs it appears that f'(c) = 0 for at least one point. f'(c) = 0 8 с (a) Figure 4.21 If a differentiable function f satisfies f(a) B U a f(c) = 0 b f(c₂) = 0 a t (b) (c) f(b), then its derivative must be zero at some points) between a and b. P(c₂)=0 9b For each of the following, first check to see if the function satisfies the three hypotheses of Rolle's Theorem on the given interval. For those that do, find all the numbers c that satisfy the conclusion of the Rolle's Theorem. 1) f(x)= x(x-1)²; [0,1] 2) f(x) = cos(4x): [ 3) f(x)=1-x; [-1,1]