Critical Points!

Find the local maximum and minimum values and saddle point(s) of the function. Graphing these is probably a good idea.

• $f(x,y) = e^{4y-x^2-y^2}$
• $f(x,y) = (1+xy)(x+y)$
• $f(x,y) = 2x^3 + xy^2 + 5x^2 + y^2$
• $f(x,y) = (x^2+y^2)e^{y^2-x^2}$
• $f(x,y) = y^2 - 2y \cos x$, $1 \leq x \leq 7$
• $f(x,y) = \sin x \sin y$, $-\pi \lt x,y \lt \pi$