Q. 33.5( 2 Votes )

f(x) = x

Answer :

We have, f(x) = x^{3}(x – 1)^{2}

Differentiate w.r.t x, we get,

f ‘(x) = 3x^{2}(x – 1)^{2} + 2x^{3}(x – 1)

= (x – 1)(3x^{2}(x – 1) + 2x^{3})

= (x – 1)(3x^{3} – 3x^{2} + 2x^{3})

= (x – 1)(5x^{3} – 3x^{2})

= x^{2} (x – 1)(5x – 3)

For all maxima and minima,

f ’(x) = 0

= x^{2}(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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