Explain why Rolle's Theorem cannot be applied to the func ? ti?on? (?? |?x| on the interva?l [? a, a]for ? ny ?a > 0.
Solution 3E Step 1 In this problem we have to give an explanation why Rolle’s theorem cannot be applied to f(x) = |x|on the interval [a,a]. Let us first see the statement of Rolle’s theorem. Rolle’s theorem: Let a < b. If f is continuous on the closed interval [a,b]and differentiable on the open interval (a,b)and f(a) = f(b)then there is a point cin (a,b) with f (c) = 0.That is under these hypotheses f has a horizontal tangent somewhere between aand b.