$f(x)=3x^2 + g(x^2) $ and x=2 is a critical point
1 Answer
It is not clear what this question is asking, but I guess you want to compute $g'(4)$ given that $x=2$ is a critical point.
Let
\[f(x)=3x^2+g(x^2).\]
Then using chain rule
\[f'(x)=6x+2x g'(x^2).\]
Substituting $x=2$ we get
\[0=f'(2)=6\cdot (2)+2\cdot 2g'(4)\]
\[\Rightarrow 12+4g'(4)=0 \Rightarrow g'(4)=-3\]
Erdos
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Let me know if you need any clarifications.
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got it man, ty, youre a savior
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