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MHT CET202411 May 2024Evening ShiftMathematicsDifferentiationActual

Let f be 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 the value of h(10) is

Options

  1. A2
  2. B1
  3. C1 2
  4. D-1

Correct answer

B. 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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