Linear Approximations and Tangent Planes. Visualize in 3-dimensions

Linear approximations and tangent planes.
Visualize in 3-dimensions

We use the level curves to help visualize the graph of a function. The z-coordinate
leaving the board is equal to the value of the function.
As a visual aid, imagine a map of elevation levels, with zero representing the lowest
point, and one through five gradually ascending to the highest point. All points in this
line have an elevation of 0; all points on that line have an elevation of 1; all points on
that line have an elevation of 2; and so on.

Then lift the blue line out of the board at distance 1 in your mind's eye. And lift the
orange line out of the board at distance 2 in your mind's eye. That's the graph of this
function.
[Graph]
It is a question of whether the graph of f, a function of x and y, is plane or curved.