Estimated Instantaneous Rate Of Change

[Veronica_Oles]

Homework Statement

You have to graph f(x) = x³ - 2x² + x and find where the instantaneous rate of change is positive negative and zero.

Homework Equations

The Attempt at a Solution

I factored this and found the zero's to be x= 0 and x = 1. With all this info given I graphed it and realized the EIRC is zero at 1 however it's also at 1/3 but I am unsure of how to obtain 1/3?

 

[arpon]

The question does not ask for the point where "$f(x)$" is positive, negative and zero, rather it asks for where "the instantaneous rate of change" is positive, negative and zero.
If $f(x)$ is zero, it does not mean that the instantaneous rate of change is also zero. For example, consider the graph of $y=x^3-2x^2+1$

Have you learned about differentiation?

 

[Veronica_Oles]

The question does not ask for the point where "$f(x)$" is positive, negative and zero, rather it asks for where "the instantaneous rate of change" is positive, negative and zero.
If $f(x)$ is zero, it does not mean that the instantaneous rate of change is also zero. For example, consider the graph of $y=x^3-2x^2+1$
View attachment 107689
Have you learned about differentiation?

I understand it now. Thank you for the great visual it helped a lot. As for writing the intervals for where it is positive, negative and zero the teacher said to estimate the values of x.