Answer :

We have, f(x) = x3(2x – 1)3


Differentiate w.r.t x, we get,


f ‘(x) = 3x2(2x – 1)3 + 3x3(2x – 1)2.2


= 3x2(2x – 1)2(2x – 1 + 2x)


= 3x2(4x – 1)


For the point of local maxima and minima,


f ’(x) = 0


= 3x2(4x – 1)= 0


= x = 0,


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


Since, x = is a point of Minima


Hence, local min value f =


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