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JEE Main 2024 · Mathematics · Differentiation and Application of Derivatives · medium

Over the closed interval [0,3], the greatest value attained by f(x)=2x^3-9x^2+12x+1 is

Single correct option

Over the closed interval [0,3][0,3], the greatest value attained by f(x)=2x3−9x2+12x+1f(x)=2x^3-9x^2+12x+1 is
  1. A. 66
  2. B. 55
  3. C. 1010
  4. D. 11
Show answer and solution

Answer: (C) 1010

f′(x)=6x2−18x+12=6(x−1)(x−2)f'(x)=6x^2-18x+12=6(x-1)(x-2), so critical points are 11 and 22. Evaluate at critical points and endpoints: f(0)=1f(0)=1, f(1)=6f(1)=6, f(2)=5f(2)=5, f(3)=10f(3)=10. The absolute maximum is 1010 at the endpoint x=3x=3; 66 is only the local maximum.
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