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JEE Main 2017 · Mathematics · Differentiation and Application of Derivatives · medium

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

Single correct option

The local maximum value of f(x)=x3−12x+5f(x)=x^3-12x+5 is
  1. A. −11-11
  2. B. 55
  3. C. 1616
  4. D. 2121
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Answer: (D) 2121

f′(x)=3x2−12=0f'(x)=3x^2-12=0 gives x=±2x=\pm2. Since f′′(x)=6xf''(x)=6x is negative at x=−2x=-2, this is a local maximum, and f(−2)=−8+24+5=21f(-2)=-8+24+5=21. The value −11-11 is the local minimum f(2)=8−24+5f(2)=8-24+5 evaluated at the wrong critical point.
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