Find the po

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.