Finding the Supremum: Solving for the Least Upper Bound of a Function

[Ted123]

Homework Statement

What is

$$\displaystyle \sup_{\substack{x\in [-1.7,1.4] \\ y\in\mathbb{R} }} \frac{2.6xy}{(y^2+1)^2}$$
(the supremum of $\displaystyle \frac{2.6xy}{(y^2+1)^2}$ over $x\in [-1.7,1.4]$ and $y\in\mathbb{R}$)?

The Attempt at a Solution

How do I find the least upper bound?

 

[susskind_leon]

Think about it: If you have a function type h(x,y)=f(x)*g(y). How would you find its maximum?