Find the points of local maxima or minima and corresponding local maximum and minimum values of `f(x)=x^3-6x^2+9x+15` . Also, find the points of inflection, if any:

Explanation

`f(x)=x^{3}-6 x^{2}+9 x+15`


`therefore f^{prime}(x)=3 x^{2}-12 x+9`


`f^{prime}(x)=0 Rightarrow 3(x^{2}-4 x+3)=0`


`Rightarrow 3(x-1)(x-3)=0`


`Rightarrow x=1,3`


Now, `f^{prime prime}`


`(x)=6 x-12=6(x-2)`


`f^{prime}(1)=6(1-2)=-6<0`


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