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AP EAMCET202315 May 2023Morning ShiftMathematicsDifferentiationActual

If f(x) is a differentiable function, f^ (x) 5 x [2,6] , f(2)=4 and f(3)=15 , then a possible value of f(6)

Options

  1. A=24
  2. Blies between 4 and 15
  3. C15
  4. D=5

Correct answer

A. =24

Step-by-step solution

Since f(3) f(2) Using Mean value theorem aligned & f^ (x)= f(3)-f(2) 3-2 = 15-4 3-2 & f^ (x)=11 & f^ (x) 5 & f(6)-f(2) 6-2 5 & f(6)-4 20 & f(6) 24 & Possible values of f(6)=24 . aligned

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