ABSTRACT
That view, from above the x-y plane, shows the product maximum (blue line) as an open (rounded) endpoint at a height 2×1 = 2. To get a better look at what is happening at the minimum (orange line), here is the view of the saddle-shaped surface from below:
The closest corner at height –1 is squared-off, because it is the result of a product of a closed endpoint and a closed endpoint, -1×1 = -1. The farther minimum ties the value at 2×-0.5 = -1, but one of the input endpoints is open, so it does not actually include –1; it approaches it as an open extreme. If both intervals span zero, then the products in opposite quadrants contend for being the extrema.
