Find three real numbers x, y, and z whose sum is 6 and the sum of whose squares is as small as possible. g

We're minimizing subject to . Using Lagrange multipliers, we have the Lagrangian



with partial derivatives



Set each partial derivative equal to 0:



Subtracting the second equation from the first, we find



Similarly, we can determine that and by taking any two of the first three equations. So if determines a critical point, then



So the smallest value for the sum of squares is when .

Answer for 2: his profit would be $2.88 explanation: you have to first multiply 72 and 0.12 together to get $8.64 once you do that you know how much money the shopkeeper made from selling the candy bars individually. so you have to do 8.64-5.76=2.88 hope that ; )answer for 3: yeah i’m sorry i have no idea what number 3 is. i’m sorry i couldn’t with that.