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AP EAMCET201923 Apr 2019Morning ShiftMathematicsApplication of DerivativesActual

In the interval ([-2,4] ), the absolute maximum of (f(x)=2 x^3-3 x^2-12 x+5 ) occurs (x= )

Options

  1. A4
  2. B-2
  3. C-1
  4. D2

Correct answer

A. 4

Step-by-step solution

Given, function (f(x)=2 x^3-3 x^2-12 x+5 ) So, (f^ (x)=6 x^2-6 x-12=0 ) [for maxima and minima (f^ (x)=0 ) ] ( aligned & x^2-x-2=0 (x+1)(x-2)=0 & x=-1,2 [-2,4] & f(-2)=-16-12+24+5=1 & f(-1)=-2-3+12+5=12 & f(2)=16-12-24+5=-15 & and f(4)=128-48-48+5=37 aligned ) The absolute maximum of (f(x) ) occurs at (x=4 ). Hence, option (a) is correct.

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