# Estimated Instantaneous Rate Of Change

1. Oct 18, 2016

### Veronica_Oles

1. The problem statement, all variables and given/known data
You have to graph f(x) = x3 - 2x2 + x and find where the instantaneous rate of change is positive negative and zero.

2. Relevant equations

3. 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???

2. Oct 18, 2016

### 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 $y=x^3-2x^2+1$