Answer :

We have, f(x) = x3(x – 1)2


Differentiate w.r.t x, we get,


f ‘(x) = 3x2(x – 1)2 + 2x3(x – 1)


= (x – 1)(3x2(x – 1) + 2x3)


= (x – 1)(3x3 – 3x2 + 2x3)


= (x – 1)(5x3 – 3x2)


= x2 (x – 1)(5x – 3)


For all maxima and minima,


f ’(x) = 0


= x2(x – 1)(5x – 3) = 0


= x =0, 1,


At x = f ’(x) changes from –ve to + ve


Since, x = is a point of Minima


At x =1 f ‘ (x) changes from –ve to + ve


Since, x =1 is point of maxima.


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