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AP EAMCET202316 May 2023Evening ShiftMathematicsApplication of DerivativesActual

The sum of the global minimum and global maximum values of the function f(x)= 4 3 x^3-4 x in [0,2] is

Options

  1. A0
  2. B8 / 3
  3. C-8 / 3
  4. D1

Correct answer

A. 0

Step-by-step solution

Given f(x)= 4 3 x^3-4 x, x [0,2] Now, f ^ ( x )=0 4 x ^2-4=0 x = 1 Now f (0)=0, f (1)= 4 3 -4=- 8 3 = global min f(-1)= -4 3 +4= 8 3 f(2)= 4 3 8-8= 8 3 global max. So sum of global max + global = 8 3 - 8 3 =0

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