Making List of Polynomial Solutions?

Questions
1

Hi CL folks!

I have an idea for an animation and came across a stuck point. Is it possible to create a list of solutions to a polynomial equation in the calculator? For example if f(x)=(x)(x-2)(x-5) and I wanted to capture a list of local max and min I could then write f '(x)=0 and a list of x values are graphed at those location. Can I make a list of those x values?

I am trying to create an animation where the vertical axis changes according to whatever polynomial a student enters, but I need to know where the local max and mins are for their equation.

Any thought? Thanks anyone for their time!

2

I don’t have a solution for you. I know how to find a critical value, but not all the critical values. I can find global extrema, but not all the local extrema. Perhaps this graph will spark an idea. Max and Min