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AP EAMCET201824 Apr 2018Morning ShiftMathematicsApplication of DerivativesActual

If f(x)= x and g(x)= 1 x for x [3,12] , then the value of c (3,12) for which f^ (c) g^ (c) = f(12)-f(3) g(12)-g(3) holds, is

Options

  1. A7.5
  2. B4.8
  3. C6
  4. D9

Correct answer

C. 6

Step-by-step solution

Given, f(x)=x^ 1 / 2 array cc f^ (x)= 1 2 x^ - 1 2 & f^ (c)= 1 2 c^ - 1 2 , & g(x)=x^ - 1 2 g^ (x)= -1 2 x^ - 3 2 & g^ (c)=- 1 2 c^ - 3 2 array Now, f^ (c) g^ (c) = f(12)-f(3) g(12)-g(3) 1 2 c^ - 1 2 - 1 2 c^ -3 / 2 = 12 - 3 1 12 - 1 3 =-c= 2 3 - 3 1 2 3 - 1 3 -c= 3 - 1 2 3 c=6

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