It is however differentiable everywhere, which means anywhere we choose to infinitely magnify the surface representing the function, the result will look like a plane. We can do this to the surface that appears in the animation by imagining that the portion of it we see lies above a rectangle on the x,y-plane. This rectangle is represented by the red rectangle in the upper left corner of the animation. This can be done repeatedly. To reset back to the initial undulating surface, click on the reset button.
Multivariable functions arise in many contexts.
For example, suppose you're a bug on the salt flats out in Utah, and suppose you don't like salt. You can't fly, so feel all around you with your antennae until you determine the direction in which it is least salty. Ok, once you determine the the direction of least saltiness you step in that direction. That means we're at a local minimum. It may not be the least salty point on the plane, but it's less salty than all the points in a local neighborhood around where we are.