if x1.x2.x3.....xn=1 where xi is positive then show that x1+x2+x3+.....+xn >=n (greater than or equal to)
Guys need your help
This was given as a problem in the chapter of Differential calculus of functions of several variables. How to solve it
if x1.x2.x3.....xn=1 where xi is positive then show that x1+x2+x3+.....+xn >=n (greater than or equal to)
Guys need your help
This was given as a problem in the chapter of Differential calculus of functions of several variables. How to solve it
This result is an easy application of the arithmetic-geometric mean inequality. But if you want to use it as an exercise in several-variable calculus, then you can regard it as asking you to find the minimum value of the function in the region , subject to the constraint It then becomes an exercise in the use of Lagrange multipliers, and you can find that the minimum value of f is n, occurring at the point
Let
Put the partial derivative with respect to equal to 0:
Multiply by to see that (because ). Thus all the 's are equal, and since their product is 1 they must all be equal to 1. Therefore the only critical point is
You can find other worked examples here.