Find the points of local maxima or minima and corresponding local maximum and minimum values of `f(x)=2//x-2//x^2,\ \ x >0` . Also, find the points of inflection, if any:

Explanation

`f(x)=\frac{-2}{x^{2}}-\frac{2}{x^{2}}(-2)=\frac{-2}{x^{2}}+\frac{4}{x^{3}}=0 `


`\frac{2}{x^{2}}=\frac{4}{x^{3}}-x=0, \frac{2}{v} `


`f^{\prime \prime}(x)=-\frac{2}{x^{3}}(-2)+\frac{4}{x^{4}}(-3)=\frac{4}{x^{3}}-\frac{12}{x^{4}} `


`f^{\prime \prime}(2)=\frac{4}{8}-\frac{12}{16}=\frac{1}{2}-\frac{3}{4}=-1 / 4<0 \text { local } `


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