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Let `f:[0,oo)vec[0,oo)a n dg:[0,oo)vec[0,oo)` be non-increasing and non-decreasing functions, respectively, and `h(x)=g(f(x))dot` If `fa n dg` are differentiable functions, `h(x)=g(f(x))dot` If `fa n dg` are differentiable for all points in their respective domains and `h(0)=0,` then show `h(x)` is always, identically zero.

A

`h(x)=0forallxge0`

B

`h(x)gt0forall xgt!=0`

C

`h(x)lt0forall xgt!=0`

D

None of these

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