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NDA 2021 Maths · Mathematics · Application of Derivatives · medium

Rolle's theorem is applicable to f(x)=|x| on [-1,1]. 2. Rolle's theorem is applicable to f(x)=x^2-1 on [-1,1].

Single correct option

Which of the statements is/are correct? 1. Rolle's theorem is applicable to f(x)=∣x∣f(x)=|x| on [−1,1][-1,1]. 2. Rolle's theorem is applicable to f(x)=x2−1f(x)=x^2-1 on [−1,1][-1,1].
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
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Answer: (B) 2 only

Rolle's theorem needs continuity on [a,b][a,b], differentiability on (a,b)(a,b) and f(a)=f(b)f(a)=f(b). ∣x∣|x| is not differentiable at 00, so statement 1 is false even though f(−1)=f(1)f(-1)=f(1). x2−1x^2-1 satisfies all conditions with f(±1)=0f(\pm1)=0, and c=0c=0; statement 2 is true.
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Original question written in the NDA 2021 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake