Find the points of local maxima or local minima, if any, using first derivative test, and local maximum or local minimum of `f(x)=1/(x^2+2)`

Explanation

`f(x)=\frac{1}{x^{2}+2} `


`f^{\prime}(x)=\frac{-2 x}{(x^{2}+2)^{2}} \Rightarrow f^{\prime}(x)=0 `


`\frac{-2 x}{(x^{2}+2)^{2}}=0 \Rightarrow x=0 `


`f(0)=\frac{1}{0+2}=1 / 2 \text { local maxima }`