Choose your own adventure

This one's for my current calculus students (others may answer in the comments hypothetically):

Given: we've now computed the slope of a tangent line to a variety of low-degree polynomials, at an arbitrary point. We've also seen a couple of applications of such slopes (minimization and velocity). One thing we've not yet done (intentionally) is made our method of computation precise.

Would you rather spend the next few days...

1. ...computing more slope formulas (for arbitrary powers and sums/differences/constant multiples of those powers...and maybe even some trig and exponential functions),

2. making our method of computing those formulas more precise, or

3. look into some more applications of slope formulas?

Keep in mind that we will do all of the above at some point soon...I just want to know where you want to go first.

What'll it be? The polls are open!