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NDA 2021 Maths · Mathematics · Application of Derivatives · medium

The function f(x)=x^4-4x^3 has a local minimum at x equal to

Single correct option

The function f(x)=x4−4x3f(x)=x^4-4x^3 has a local minimum at xx equal to
  1. A. 33
  2. B. 00
  3. C. 44
  4. D. 11
Show answer and solution

Answer: (A) 33

f′(x)=4x3−12x2=4x2(x−3)f'(x)=4x^3-12x^2=4x^2(x-3), which vanishes at x=0x=0 and x=3x=3. The sign of f′f' does not change at 00 (it stays negative), so x=0x=0 is not an extremum; at 33 it changes from negative to positive, a local minimum.
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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