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NDA 2018 Maths · Mathematics · Derivatives · medium

For f(x)=1/x on [1,4], the value of c in Lagrange's mean value theorem is

Single correct option

For f(x)=1xf(x)=\frac1x on [1,4][1,4], the value of cc in Lagrange's mean value theorem is
  1. A. 52\frac52
  2. B. 2\sqrt2
  3. C. 22
  4. D. 33
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Answer: (C) 22

The mean slope is 14−13=−14\frac{\frac14-1}{3}=-\frac14. Since f′(c)=−1c2f'(c)=-\frac1{c^2}, we need c2=4c^2=4, so c=2∈(1,4)c=2\in(1,4). The midpoint 52\frac52 is not the answer because ff is not linear.
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Original question written in the NDA 2018 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