Sketch the curve y=x(x-2)^3 showing any stationary points and points of inflection

Step-by-step explanation:

hello :

let   :   y=f(x)

f(x)==x(x-2)^3   so : f'(x) = 1.(x-2)^3+3x(x-2)²

f'(x) = (x-2)²(x-2+3x)

f'(x) = (x-2)²(4x-2)

f'(x) =0    : x=2  or x=1/2

the minumum is (1/2 ,f(2))

the inflection points use f"(x) = 0continu

found it xd it ok yt