Extrema ICE Math21aFind all the critical p oints of f(x, y) = x5y + xy5+ xy and classify them.1) Find the gradient ∇f (x, y).2) Find the critical points ∇f(x, y) = (0, 0).3) Find the discriminant D at each critical point.4) If D > 0, find the sign of H11.5) Classify the critical points.21a Hatsumon: Mountain Peaks, Sinks and Passes O. Knill, 10/23/2003You are on a circular island surrounded by sea. You count A mountain peaks, B sinksand C mountain passes. You observe that A + B − C = 1. Can you see why this is truefor any island?The example shows the Hawaii main island. On a rough scale, we have A = 7 mountainpeeks, B = 1 sinks and C = 7 mountain passes.1) Explore the rule with simple examples.2) Look what happens if you deform a given island to an island, with only one mountain and nosink and no mountain pass.3) Can you see what happens during the
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