(a): Let /(21, 12..., ) = V8182 --.In. Suppose , > 0 for i = 1,...,n. . Maximize / subject to Ed, =c. . Deduce that /8102.., & atanto +, This is an important inequality, called the arithmetic-geometric mean inequality (AM-GM). (b): 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 (0, 0,0)). Suppose the temperature at the point (1, 2, 2) is 100. . Find the rate of change of the temperature at the point (-1,2, -2) in the direction o (2, 1,3). . Show that, at any point in the sphere, the direction of greatest increase in temperature is given by a vector that points toward the origin