Recall that the derivative of a function will give you a function of it's rate of change. i.e. it's slope at a given value x.
So, we need to find all values of x where the derivatives of each function are equal.
The derivative of x^2 is 2x
The derivative of x^3 is 3x^2
Set these equal to each other and solve for x
3x^2 = 2x
3x^2 - 2x = 0
x(3x - 2) = 0
So x = 0 or 3x - 2 = 0
3x - 2 = 0
3x = 2
x = 2 / 3
Therefore, our two possible values of x are 0 and 2/3.
