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If f x is a twice differentiable function such that f " x = - f x , f ' x = g x , h x = f 2 x + g 2 x and h 10 = 10 , then h 5 is equal to

Options

  1. A5
  2. B15
  3. C10
  4. D17

Correct answer

C. 10

Step-by-step solution

h ' x = 2 f ⋅ f ' + 2 g g ' = 2 f ⋅ f ' + 2 f ' f "   ( ∵ g = f ' ) = 2 f ⋅ f ' + 2 f ' - f = 0 ∴ h ' x = 0 ⇒ h x is a constant function ∴   h x = 10 ⇒   h 5 = 10

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