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NDA 2019 Maths · Mathematics · Derivatives · medium

If f(x)=(x^2+1)/(x-2), then f'(3) is equal to

Single correct option

If f(x)=x2+1x−2f(x)=\dfrac{x^2+1}{x-2}, then f′(3)f'(3) is equal to
  1. A. 44
  2. B. −10-10
  3. C. −4-4
  4. D. −12-\frac{1}{2}
Show answer and solution

Answer: (C) −4-4

By the quotient rule, f′(x)=2x(x−2)−(x2+1)(x−2)2=x2−4x−1(x−2)2f'(x)=\frac{2x(x-2)-(x^2+1)}{(x-2)^2}=\frac{x^2-4x-1}{(x-2)^2}. At x=3x=3: 9−12−11=−4\frac{9-12-1}{1}=-4. The value f(3)=10f(3)=10 is not the derivative, and reversing the order in the numerator would change the sign.
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Original question written in the NDA 2019 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