# A trigonometric polynomial.

.

This function is defined on and is periodic with period equal to ; therefore we can study it on .

Because of the periodicity, the function has no limit at . Moreover, there is no other open endpoint of the domain and the function is continuous on , therefore we have no limit to compute.

The function is given by a trigonometric polynomial, thus it is differentiable on , whence on .

Where does the first derivative vanish?

Noah Dana-Picard 2007-12-28