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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