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AP EAMCET201726 Apr 2017Morning ShiftMathematicsApplication of DerivativesActual

For the function f(x)=(x-1)(x-2) defined on [0, 1 2 ] , the value of c satisfying Lagrange's mean value theorem is

Options

  1. A1 5
  2. B1 3
  3. C1 7
  4. D1 4

Correct answer

D. 1 4

Step-by-step solution

Given function, f(x)=(x-1)(x-2) =x^2-3 x+2 and x [0, 1 2 ] By using Lagrange's mean value theorem, aligned & f^ (c)= f(b)-f(a) b-a = f ( 1 2 )-f(0) 1 2 -0 & 2-3= (- 1 2 ) (- 3 2 )-(-1)(-2) - & 2 c-3=2 ( 3 4 -2 ) & 2 c-3=- 5 2 & 4 c-6=-5 & c= 1 4 (0, 1 2 ) aligned

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