Find all the points of local maxima and local minima of the function `f(x)=x^3-6x^2+12 x+15` .

Explanation

`f(x)=x^{3}-6 x^{2}+9 x+15 `
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therefore f^{prime}(x)=3 x^{2}-12 x+9 `
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f^{prime}(x)=0 Rightarrow 3(x^{2}-4 x+3)=0 `
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Rightarrow 3(x-1)(x-3)=0 `
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Rightarrow x=1,3 `

Now, `f^{prime prime} `
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(x)=6 x-12=6(x-2) `
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f^{prime}(1)=6(1-2)=-6<0 `
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