By that I think x +1/y would work

Well, if you're ever unsure of an answer, you can always check it yourself. Let's see if it fulfills all of the necessary criteria. For any x > 0 and y > 0, we have f(x, y) = x + 1/y. Obviously, x is positive, and we can easily see that 1/y can only be negative if y < 0, which we've temporarily disallowed. Hence, we have f(x, y) = (positive) + (positive) = (positive). So it satisfies the first criterion. Great!

Next, let's check the partial derivative with respect to x. f[SUB]x[/SUB] = 1. One is always positive, no matter what, so we're good here too.

Finally, let's check the partial derivative with respect to y. f[SUB]y[/SUB] = -1/y[SUP]2[/SUP]. We know that y[SUP]2[/SUP] is always going to be positive, so we have f[SUB]y[/SUB] = (negative)/(positive) = (negative). Hooray! The function passes all three criteria!

The question only asks you to find one example of a function which satisfies the criteria, and you've done just that. So, problem solved. Good job.