So for my formula for F', is there something specific I have to write for x=1 and x=2? How would I do that since my intervals are 0<= x <= 1 and 1<x<2 and x>=2 where there's ones and twos overlapping?
But doesn't the Fundamental Theorem of Calculus tell us that since our F is continuous everywhere, that it should be differentiable there? How do I show that x=1,2 are not differentiable? I know if the limit from the left and right are equal, it is continuous at that point.
I think I actually understood that better than I thought and was just getting confused by my own writing. Thank you so much. I know you've already helped alot, but do you have any ideas about how I would then find a formula for F'(x) wherever F is differentiable? My test is tomorrow, that is the...
F(x)= x if 0 <= x <= 1.
Then, for 1< x <2, we're taking the integral of 0, so I should just get a constant?
I just don't know how I am supposed to write that part of the third part whre x>=2
Should I be using limits? I actually did graph it. I know what the F(x) should be, I'm just not sure how to rigorously show it using a theorem, formula, etc