calc 3

3: Let r, y and 2 be three positive numbers whose sum is a xed number 5'. a) Use Lagrange multipliers to show that the product of these three positive numbers is maximum if they are the same. b) Using part a), show that the geometric mean of any three posi tive numbers is less than or equal to the arithmetic mean. That is, show that $+y+z 3mng 3