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Let f : (-5,5)rarrR be a differentiable ...

Let `f : (-5,5)rarrR` be a differentiable function of with `f(4) = 1, f'(4)=1, f(0) = -1 and f'(0) =1 If, g(x)=(f(2f^(2)(x)+2))^(2),` then g'(0) equals

A

4

B

-4

C

8

D

-8

Text Solution

Verified by Experts

`g'(x)=2f(2f^(2)(x)+2)xxf'(2f^(2)(x)+2)xx4f(x)cdotf'(x)`
`therefore" "g'(0)=2f(2f^(2)(0)+2)xxf'(2f^(2)(0)+2)xx4f(0)cdotf'(0)`
`=2f(4)cdotf'(4)cdot4f(0)f'(0)`
`=2xx4(-1)(1)`
`=-8`
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