Question

1. Explain why Rolle's theorem is no
intervals.
(i) f(x) =
f(0) = 4, tel-1,1​

Answer 1

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• The Rolle's theorem fails here because f(x) is not differentiable over the whole interval (−1,1). Figure 4. The linear function f(x)=x is continuous on the closed interval [0,1] and differentiable on the open interval (0,1). This is explained by the fact that the 3rd condition is not satisfied (since f(0)≠f(1).)

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