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{a}: let shn... Hag?) = {ya-lag\" an. Suppose at! 'e 0 fort = 1.... .11. I Maximise f subject to 23:13!- =c. I Deduoe that rm; .. urn 5 W. This is an important inequality1 called the arithmetic-geometric mean inequality [AM-GM]. {h}: The temperature T in a metal sphere is inversely proportional to the distance from the cen- ter of the sphere {assume the sphere is centered at the origin [13,11]. [ll]. Suppose the temperature at the point {1.2.2} is 100. I: Find the rate of change of the temperature at the point (1.2. 2) in the direction of [2.1.3]. a Show that1 at any point in the sphere1 the direction of greatest morease in temperature is given by a vector that points toward the origin