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Find the points of local maxima and mini...

Find the points of local maxima and minima of the function f given by ` f(x)= x^(3)-12x^(2)+36x+5` .

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` f(x)= x^(3)-12x^(2)+36x+5`
`f'(x)=3x^(2)-24x+36`
`=3(x^(2)-8+12)`
`=3(x-2)(x-6)`
x=2,6 are critical points .

With respect to ` x=2, (dy)/(dx)` changes sign from positive to negative , hence x=2 is point of local maxima and w.r.t. x=6 , f'(x) changes sign from negative to positive hence x=6 is point of local minima.
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