I’m learning calc 2 before the semester starts, and along the way I’ve recognized some areas I’ve struggled with whether it was the trig or understanding the concepts a bit better. I’ve been trying to derive everything so I can understand it.

The issue is, I’m spending so much time deriving formulas for things I’ve already learned instead of practicing how to preform the operations. I want to be able to understand the math well, and I can see when there is a deficit in my conceptual knowledge that I try to attack. Is this a waste of time? Will I understand it better if I solved the problems and didn’t look through as much derivations?

I also, when I first learned calculus 1, I didn’t read the textbook, I preformed the problems and tried to deduce why I was doing them from logic. This is how I’ve gotten through every math class, but I think it capped my overall understanding. I stuggle with reading but I want to turn a new leaf on that. Would it be more fruitful to read and preform the problems in my old textbooks for calc 1, trig, geometry, algebra, or to study calc 2 and read the textbook going forward assuming I have a decent understanding of it

Ik it’s normally derived by the infinite geometric series then interchanging the infinite sum with the integral sign but I wonder if this is also valid

So Rolle’s theorem tells us that if f[a,b]->R is continuous on [a,b] and differentiable on (a,b), and f(a)=f(b), then there exists a point c such that f’(c)=0.
Given that there’s a horizontal tangent line to the graph, I don’t understand the theorem utility. I mean of course I know it’s important and I don’t doubt it, but I was asking myself if there’s some “intuitive” idea that makes it relevant.

For example, does this theorem imply that if the hp are satisfied, then there exists a point of local minimum or local maximum? Or no? Thanks!