Test whether a function ever descends at $80^\circ$ or more

26 Views Asked by At

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)