Find all critical points and classify them as local maxima, local minima, saddle points, or none of these.
f(xy)=1+2x^2−cos(4y)

(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.)

Question

Find all critical points and classify them as local maxima, local minima, saddle points, or none of these.
f(xy)=1+2x^2−cos(4y)

(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.)