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MHT CET20239 May 2023Evening ShiftMathematicsApplication of DerivativesActual

The maximum value of the function f(x)=3 x^3-18 x^2+27 x-40 on the set S = x R / x^2+30 11 x is

Options

  1. A122
  2. B132
  3. C112
  4. D222

Correct answer

A. 122

Step-by-step solution

aligned & S = x R / x^2+30 11 x & x^2+30 11 x & x^2-11 x+30 0 & (x-5)(x-6) 0 & x [5,6] aligned Now, f (x)=3 x^3-18 x^2+27 x-40 aligned f ^ (x) & =9 x^2-36 x+27 f ^ (x) & =9 (x^2-4 x+3 ) & =9 [ (x^2-4 x+4 )-1 ] & =9(x-2)^2-9 aligned f ^ (x)>0 x [5,6] f (x) is strictly increasing in the interval [5,6] Maximum value of f (x) when x [5,6] is f(6)=122

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