how do I graph this using the first and second derivative and three sign charts.

Question

i have to label the inflection point, extreme values and the intercepts also.

f(x)= x^3-6x^2

Answer 1

slope = 3 x^2 -12 x =3 x (x-4)

second derivative (curvature)
= 6 x - 12

so the slope is 0 at x = 0 and at x = 4

at x = 0
is that a min or a max or in inflection point?
second derivative = -12
That is a maximum, starts down from there

at x = 4 is that a min or a max or an inflection point?
second derivative = +12
so that is a minimum, starts up fro there.

Answer 2

Oh, intercepts
y = x^3-6x^2
0 = x^2 (x-6)
bounced off x axis at x = 0
crossed x axis at x = 6