`f(x) = tan(x), [0,pi]` Determine whether Rolle’s Theorem can be applied to `f` on the closed interval `[a, b]`. If Rolle’s Theorem can be applied, find all values of `c` in the open...

`f(x) = tan(x), [0,pi]` Determine whether Rolle’s Theorem can be applied to `f` on the closed interval `[a, b]`. If Rolle’s Theorem can be applied, find all values of `c` in the open interval

Expert Answers
Borys Shumyatskiy eNotes educator| Certified Educator

NO. This function isn't defined on entire interval (the point where it isn't defined is pi/2).

Actually, not only Rolle's Theorem isn't applicable but also its conclusion doesn't hold: there is no point where f'(x)=0.