Please help with the problem.

(a): Let /(21, 12. .. .. In) = $2142 ..In. Suppose I; > 0 for i = 1,. .., n. . Maximize / subject to )_ 2, = c. . Deduce that /5152.In c Stat at In. 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 of (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