that the curve looks like (x-2)^3 close tp x=2, and so we expect this point
to be a point of inflection.
Also as x goes to +/- infinity y goes to +infinity.
Now lets look for the stationary points:
dy/dx= (x-2)^3 + 3 x (x-2)^2 = (x-2)^2 [(x-2) + 3x]=2 (x-1) (2x -1)
Which is equal to zero when x=1/2, and when x=2. Then we can deduce
from shape of the cureve and the position of the zeros of y, that x=1/2 is a
minimum, and x=2 a point of inflection (we could confirm this with the
second derivative test if we wanted).
y~=-1.68, at the minima corresponding to x=1/2.
Putting this all together we get something like the attachment.