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AP EAMCET201823 Apr 2018Evening ShiftMathematicsApplication of DerivativesActual

The sum of the maximum and the minimum values of 3 x^4-2 x^3-6 x^2+6 x+4 , in (0,2) is

Options

  1. A28
  2. B167 16
  3. C134 15
  4. D87 16

Correct answer

B. 167 16

Step-by-step solution

Let a function f(x)=3 x^4-2 x^3-6 x^2+6 x+4 So, aligned f^ (x) & =12 x^3-6 x^2-12 x+6 & =6(x-1)(x+1)(x-1 / 2 aligned For maxima and minima array rlrl f^ (x) & =0 x & =1, 1 2 , [ -1 (0,2] & Now, and & f(1) & =5 (minimum) & & f(1 / 2) & = 87 16 (maximum) array Now, f(1)=5 (minimum) and f(1 / 2)= 87 16 (maximum) So, f(1)+f ( 1 2 )= 167 16 .

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