Let $$f(x,y) = 1+x^{2}-\cos\!\left(4y\right).$$ Find all critical points and classify them as local maxima, local minima, saddle points, or none of these.

critical points:
(give your points as a comma separated list of (x,y) coordinates. if your answer includes points that occur at a sequence of values, e.g., at every odd integer, or at any constant multiple of another value, use m for any non-zero even integer, n for any non-zero odd integer, and/or k for other arbitrary constants.)

classifications:
(give your answers in a comma separated list, specifying maximum, minimum, saddle point, or none for each, in the same order as you entered your critical points)