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NDA 2025 Maths · Mathematics · Application of Derivatives · medium

The local maximum value of f(x)=2x^3-9x^2+12x+5 is

Single correct option

The local maximum value of f(x)=2x3−9x2+12x+5f(x)=2x^3-9x^2+12x+5 is
  1. A. 99
  2. B. 1010
  3. C. 55
  4. D. 1414
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Answer: (B) 1010

f′(x)=6x2−18x+12=6(x−1)(x−2)f'(x)=6x^2-18x+12=6(x-1)(x-2). Since f′′(x)=12x−18f''(x)=12x-18 is negative at x=1x=1, the local maximum is at x=1x=1: f(1)=2−9+12+5=10f(1)=2-9+12+5=10. The value 99 is f(2)f(2), the local minimum, and 55 is f(0)f(0). Always test the sign of f′′f'' before naming the nature of a point.
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