Question

Find the values of x for which f(x) = [x(x − 2)]2 is an increasing function. Also, find the
points on the curve, where the tangent is parallel to x-axis.

Answer 1

\[\Large\bf\sf f(x)\quad=\quad \left[x(x-2)\right]^2\]So for the first part:
In order to find intervals of increasing/decreasing, we need to find critical points.
Do you remember how to do that? :o

Answer 2

I assume this is for Calculus, yes? :)

Answer 3

could you help me

Answer 4

Can you answer my questions..?

Answer 5

linear function

Answer 6

f'=2(x)(x-2)^2+2(x-2)x^2=2x(x-2)(x-2+x)
f'=4x (x-1)(x-2) =0
x=0 , 1,2