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If f is the function whose graph is shown, let h(x) = f(f(x)) and g(x) = f(x2).
I am having problems with g'(2). 

If f is the function whose graph is shown let hx ffx and gx fx2I am having problems with g2 class=

Respuesta :

LammettHash
By the chain rule,

[tex]g(x)=f(x^2)\implies g'(x)=2xf'(x^2)[/tex]

so

[tex]g'(2)=2\times2\times f'(2^2)=4f'(4)[/tex]

You were able to find [tex]h'(2)=f'(f(2))\times f'(2)[/tex], which requires knowing both [tex]f(2)[/tex] and [tex]f'(2)[/tex]. Do you also happen to know [tex]f(4)[/tex] and [tex]f'(4)[/tex]?

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