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Discuss the applicability of Rolle’s theorem on the function f (x) = Asked by Topperlearning User | 04 Aug, 2014, 04:11: PM Expert Answer

Since a polynomial function is everywhere continuous and differentiable. Therefore, f (x) is continuous and differentiable at all points except possibly at x = 1.

Now, we consider the differentiability of f (x) at x = 1.
We have,
(LHD at x = 1) = [f (x) = x2 + 1 for 0 ≤ x ≤ 1]

(RHD at x = 1) = \ (LHD at x = 1) ¹ (RHD at x = 1)
So, f (x) is not differentiable at x = 1.
Thus, the condition of a differentiability at each point of the given interval is not satisfied.
Hence, Rolle’s theorem is not applicable to the given function on the interval [0, 2].
Answered by | 04 Aug, 2014, 06:11: PM

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