I'm designing a roller coaster and the constraint is that it can't go down at a higher angle than $80^\circ$. I tried using integrals, but the problem is that I have to manually set the bounds. Anything that can help? double integrals or something?
Basically $$f '(x)>\tan\left(\dfrac{5\pi}{9}\right)$$
(it will be a piece-wise function)