I hope someone can help. I'm trying to find the x-coordinate for the turning point (circled in red) within my drawing:
This drawing is based on the equation f(x) = x^3-2x^2+x
I need to know this x-coordinate in order for me to accurately state the intervals where the rate of change is positive and negative. Since turning points indicate an opposite change in slope, I therefore need to know what the x-coordinate of this turning point is.
I know that it's a cubic function that has a positive leading coefficient, therefore having an end behaviour that extends from quadrant 1 to quadrant 3. I also know that the roots are x = 0 and x = 1 (with a multiplicity of 2). I also know that I could use graphing technology (e.g. Demos), but I want to know if there's a simple way to find the x-coordinate for this turning point algebraically.