Find the points of local maxima or minima and corresponding local maximum and minimum values of `f(x)=x^3-2a x^2+a^2\ x` , `a >0,\ \ x in R` . Also, find the points of inflection, if any:

Explanation

Given function: `f(x)=x^{3}-2 a x^{2}+a^{2} x`

Differentiating with respect to `x`

`f^{prime}(x)=3 x^{2}-4 a x+a^{2}`

Again differentiating with respect to `x`

`f^{prime prime}(x)=6 x-4 a`

For maxima and minima

Put `f^{prime}(x)=0`

`Rightarrow 3 x^{2}-4 a x+a^{2}=0 `

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