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NDA 2020 Maths · Mathematics · Application of Derivatives · medium

The local maximum value of the function f(x)=x^3-6x^2+9x+2 is

Single correct option

The local maximum value of the function f(x)=x3−6x2+9x+2f(x)=x^3-6x^2+9x+2 is
  1. A. 66
  2. B. 22
  3. C. 11
  4. D. 99
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Answer: (A) 66

f′(x)=3x2−12x+9=3(x−1)(x−3)f'(x)=3x^2-12x+9=3(x-1)(x-3), and f′′(x)=6x−12f''(x)=6x-12. At x=1x=1, f′′=−6<0f''=-6<0, so x=1x=1 gives the local maximum f(1)=1−6+9+2=6f(1)=1-6+9+2=6. At x=3x=3, f′′>0f''>0, so f(3)=27−54+27+2=2f(3)=27-54+27+2=2 is the local minimum value. The option 11 is the location of the maximum, not its value. Do not confuse the point with the value, or the maximum with the minimum.
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Original question written in the NDA 2020 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