For the function g(x)=x^3-2x^2-1, at what tangent point is the instantaneous rate of change equal to -1?

The derivative of the function is

3x^2 - 4x....set this equal to  - 1   and solve for x

3x^2 - 4x  = -1    

3x^2 - 4x + 1    =    0

(3x - 1) ( x - 1)   = 0

Setting each factor to 0 and solving for x produces

 x = 1/3       or         x  = 1

And when x = 1/3, y = -32/27

And when x = 1, y = -2

So.....we have two points where this is true

(1/3, -32/27)    and ( 1, - 2 )