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JEE Advanced2006MathematicsDifferentiationActual

If f^ (x)=-f(x) , where f(x) is a continuous double differentiable function and g(x)=f^ (x) . If F(x)= (f ( x 2 ) )^2+ (g ( x 2 ) )^2 and F(5)=5 , then F(10) is

Options

  1. A0
  2. B5
  3. C10
  4. D25

Correct answer

B. 5

Step-by-step solution

As, f(x)=-f(x) d d x (f^ (x) )=-f(x) g^ (x)=-f(x) and f^ (x)=g(x) where, F^ (x)=2 (f ( x 2 ) ) f^ ( x 2 ) 1 2 +2 (g ( x 2 ) ) g^ ( x 2 ) 1 2 =0 [using Eq. (1)] F(x) is constant F(10)=F(5)=5

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