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AP EAMCET201822 Apr 2018Morning ShiftMathematicsApplication of DerivativesActual

The constant ' C ' of Lagrange's mean value theorem for the function f(x)= 2 x+3 4 x-1 defined on [1,2] is

Options

  1. A1+ 15 3
  2. B1+ 21 4
  3. C5 3
  4. D3 2

Correct answer

B. 1+ 21 4

Step-by-step solution

Using mean value theorem, we have aligned f^ (c) & = f(2-f(1) 2-1 -14 (4 c-1)^2 & = 1- 5 3 1 aligned aligned & -14 (4 c-1)^2 =- 2 3 & (4 c-1)^2=21 & (4 c-1)= 21 & 4 c=1+ 21 or 4 c=1- 21 & c= 1+ 21 4 [ c= 1- 21 4 [1,2] ] & aligned

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