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MHT CET202012 Oct 2020Evening ShiftMathematicsApplication of DerivativesActual

If the L. M. V. T. holds for the function f(x)=x+ 1 x , x [1,3] , then c=

Options

  1. A3
  2. B3
  3. C2
  4. D- 3

Correct answer

A. 3

Step-by-step solution

Given f(x)=x+ 1 x and LMVT holds f^ (x)=1- 1 x² f^ (c)=1- 1 c² f(1)=1+1=2 and f(3)=3+ 1 3 = 10 3 f^ (c)=1- 1 c² = 10 3 -2 (3-1) 1- 1 c² = 4 3(2) = 2 3 1 c² =1- 2 3 = 1 3 c²=3 c= 3

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