$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
\[0=f'(2)=6\cdot (2)+2\cdot 2g'(4)\]
\[\Rightarrow 12+4g'(4)=0 \Rightarrow g'(4)=-3\]

4.8K
-
Let me know if you need any clarifications.
-
got it man, ty, youre a savior
-
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- 1 Answer
- 472 views
- Pro Bono
Related Questions
- Not sure what I'm doing wrong
- Question 1 calculus
- A function satifying $|f(x)-f(y)|\leq |x-y|^2$ must be constanct.
- Prove the trig identity $\sec x- \sin x \tan x =\frac{1}{\sec x}$
- Measure Theory and the Hahn Decomposition Theorem
- Volume of the solid of revolution for $f(x)=\sin x$
- Optimization Quick Problem
- Find $\lim _{x \rightarrow 0} x^{x}$