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MHT CET20243 May 2024Morning ShiftMathematicsDifferentiationActual

Let f be a twice differentiable function such that f ^ (x)=- f (x), f ^ (x)= g (x) and h (x)=[ f (x)]^2+[ g (x)]^2 . If h (5)=1 , then h (10) is

Options

  1. A2
  2. B4
  3. C-1
  4. D1

Correct answer

D. 1

Step-by-step solution

aligned h (x) & =[ f (x)]^2+[ g (x)]^2 ~h ^ (x) & =2[ f (x)] f ^ (x)+2[ ~g (x)] g ^ (x) & =2 [- f ^ (x) ] f ^ (x)+2 [ f ^ (x) ] f ^ (x) & =0 aligned h (x) is a constant function. h(5)=1 h(10)=1

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