Maximization of $x+y$ when each is greater than $1$ and $xy = 16$. The product of two numbers $x$ and $y$ is $16$. We know $x\ge 1$ and $y\ge 1$. What is the greatest possible sum of the two numbers?

Hint:
Since $x \cdot y = 16$  and $x,y \geq 1 > 0$ we have $y = \frac{16}{x}$. Now can you find the maximum of the function
$$f(x) = x + \frac{16}{x}$$
for $x \geq 1$ and $\frac{16}{x} \geq 1$?
