Please help with practice problems 1, 2, and 3.

1) Let k E R and f(a:, y) = $2 + 312 + kmy. If you imagine the graph changing as 1:: increases, at what values of 1:: does the shape of the graph change qualitatively? Justify your answer. 2) Letf(:1:,y) = 5316'\" e53 315. (a) Show that f has a unique critical point and that this point is a local maximum for f. (b) Show that f is unbounded on the yaxis, and thus has no global maximum. (Note that for a differentiable function g (3:) 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.) 3) Suppose that a pentagon is composed of a rectangle topped by an isosceles triangle. If the length of the perimeter is xed, nd the maximum possible area. Assume that the sides of the triangle that are required to be same length do not share a side with the rectangle