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NDA 2023 Maths · Mathematics · Application of Derivatives · medium

The function f(x)=x^2e^-x has a local maximum at x equal to

Single correct option

The function f(x)=x2e−xf(x)=x^2e^{-x} has a local maximum at xx equal to
  1. A. 00
  2. B. 22
  3. C. 11
  4. D. −2-2
Show answer and solution

Answer: (B) 22

f′(x)=e−x(2x−x2)=0f'(x)=e^{-x}(2x-x^2)=0 gives x=0x=0 or x=2x=2. Since f′f' changes from positive to negative at x=2x=2, it is a local maximum; at x=0x=0 the sign changes from negative to positive, so it is a local minimum. The value 00 is therefore the trap.
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Original question written in the NDA 2023 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