AM-GM Optimization Principle

AM-GM Optimization Principle

For positive real numbers:

$$x_1,x_2,\ldots,x_n$$

$$\frac{x_1+x_2+\cdots+x_n}{n}\geq\sqrt[n]{x_1x_2\cdots x_n}$$

Equality holds when:

$$x_1=x_2=\cdots=x_n$$

Usage

- Used to obtain maximum products and minimum sums without explicitly differentiating.