Graph the potentials in Probs. 7 and 9 and for two other functions of your choice as surfaces over a rectangle in the xy-plane. Find the locations of the maxima and minima by inspecting these graphs.

Data from Prob. 7

Verify (3) in Theorem 2 for the given Φ(x, y), (x₀, y₀) and circle of radius 1.

(x - 1)( y - 1), (2, -2)

Data from Prob. 9

Verify (3) in Theorem 2 for the given Φ(x, y), (x₀, y₀) and circle of radius 1.

x + y + xy, (1, 1)