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Find the points of maximum ( local maximum ) and minimum ( local minimum ) of the function ` f(x)=x^(3)-3x^(2)-9x ` ?

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Verified by Experts

Here , `f(x)=3x^(3)-9x`
`f'(x)=3x^(2)-6x-9`
For point of maxima and minima
`implies x^(2)-2x-3=0`
`implies (x-3)(x+1)=0`
x=3 , x=-1
Using second derivative test :
`f''(x)=6x-6`
` f''(3)=12,f''(-1)=-12`
Hence x=3 is point of local minimum and x=-1 is point of local maximum.
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