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.

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.

zepdrix · Answer

$$\Large\bf\sf f(x)\quad=\quad \left[x(x-2)\right]^2$$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

zepdrix · Answer

I assume this is for Calculus, yes? :)

anonymous · Answer

could you help me

zepdrix · Answer

Can you answer my questions..?

anonymous · Answer

linear function

amoodarya · Answer

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|dw:1388384522760:dw|