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

Let `f: (-5,5) rarr R` be a differentiable function 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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