Answer :

f(x)=(x-1)(x-2)2=x2-4x+4 * x-1= x3-4x2+4x-x2+4x-4


f(x)=x3-5x2+8x-4


f’(x)=3x2-10x+8


f’(x)=3x2-6x-4x+8


=3x(x-2)-4(x-2)


=(3x-4)(x-2)



Function f(x) is decreasing for x [4/3,2] and increasing in x (-∞,4/3) (2, ∞)


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