Find the points of local maxima or minima and corresponding local maximum and minimum values of `f(x)=(x+1)(x+2)^(1//3),\ \ xgeq-2` . Also, find the points of inflection, if any:

Explanation

Given function: `f(x)=(x+1)(x+2)^{1 / 3}, x geq-2`

Differentiating with respect to `x`

`f^{prime}(x)=(x+2)^{1 / 3}+1 / 3(x+1)(x+2)^{-2 / 3}`

`=(x+2)^{-2 / 3}(x+2+1 / 3(x+1))`

`=1 / 3(x+2)^{-2 / 3}(4 x+7)`

Again differentiating with respect to `x`

`f^{prime prime}(x)=-2 / 9(x+2)^{-5 / 3}(4 x+7)+1 / 3(x+2)^{-2 / 3} times 4`

For maxima and minima

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