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

Guest Nov 24, 2018

#1**+2 **

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 )

CPhill
Nov 24, 2018