Find the points of local maxima or minima and corresponding local maximum and minimum values of `f(x)=(x-1)(x+2)^2` . Also, find the points of inflection, if any:

Explanation

`f(x)=(x-1)(x+2)^{2}=(x-1)(x^{2}+4 x+4)`


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


`f^{prime}(x)=3 x^{2}+6 x-ldots-(11)`


`f^{prime}(x)=0, quad 3 x^{2}+6 x=0`


`quad 3 x(x+2)=0`


`x=0,-2`


`f^{prime prime}(x)=6 x+6-cdots-text { (II) }


text { at } x=-2, f^{prime prime}(-2)=6(-2)+6=-6 leq 0`


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