On a good number of questions. I realize I'm new here, but I hope to stick around. I have left a more sizable message after the problems, in case you're interested.

Here goes:

:1. "For what values of k does the graph of y=(4/3)x^3+2kx^2+5x+3 have two tangent lines parallel to the x-axis."

This is the part of an exorbitant amount of problems that I have been working on that I don't know how to do and couldn't find any help for on Wikipedia or by searching google for teacher's notes and the like.

Anyways, even if you only want to tackle one problem, I would be greatly appreciative.

I also wanted to say that I have been shadowing this forum for a while, and would like to start contributing.

Thanks for any help you can provide.