From Hardcover Book, Marsden/Tromba, Vector Calculus Let f(x, y) = 5ye^x - e^5x - y^5
A) Show that f has a unique critical point and that this point is a local maximum for f.
B) Show that ff is unbounded on the y-axis, and thus has no global maximum. (Note that for a differentiable function g(x) of a single variable, a unique critical point which is a local extremum is necessarily a global extremum. This example shows that this is not the case for functions of several variables).