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AP EAMCET202315 May 2023Morning ShiftMathematicsApplication of DerivativesActual

If A = x / 9 x x ^2+20 and f : A R is defined by f(x)=2 x^3-15 x^2+36 x-48 , then the maximum value of f(x) is

Options

  1. A-20
  2. B7
  3. C20
  4. D-16

Correct answer

B. 7

Step-by-step solution

aligned & Given A = x: 9 x x ^2+20 & A = x: x [4,5] =[4,5] & Given f(x)=2 x^3-15 x^2+36 x-48 & f^ (x)=6 (x^2-5 x+6 )=6(x-3)(x-2) aligned For maxima or minima f^ (x)=0 aligned & x=3,2 & but A=[4,5] aligned Hence f(x) is increasing function in A =[4,5] Therefore maximum value of f(x) will be obtained at x=5 f(5)=7

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