Find symmetry of f (x) = x^3 - 2x^2 -15x +18?

Question

I already ask and there is an answer but I don't understand. Because there is some things that confusing me. Plz helping me again....

Answer 1

Okay, differentiating x^3 - 2x^2 -15x +18 once will give you the tangent slope as a function of x. Differentiating it twice will give you the rate of change of tangent slope as a function of x. When this rate of change of tangent slope is 0, then you have the inflexion point of the function. For cubics, this inflexion point is the point of symmetry.

f ' (x) = 3x^2 -4x -15

f ' ' (x) = 6x -4

Setthing this to 0, we have

6x - 4 = 0

x = 2/3

f(2/3) = 200/27

So, the coordinates of the point of symmetry for this function is

(2/3, 200/27)