Visualizing Linear Approximations and Tangent Planes in 3D

p {margin: 0; padding: 0;} .ft00{font-size:20px;font-family:Arial;color:#000000;} .ft01{font-size:18px;font-family:ArialMT;color:#000000;} .ft02{font-size:18px;line-height:23px;font-family:ArialMT;color:#000000;} Linear approximations and tangent planes. Visualize in 3-dimensions We use the level curves to help visualize the graph of a function. The z-coordinateleaving the board is equal to the value of the function. As a visual aid, imagine a map of elevation levels, with zero representing the lowestpoint, and one through five gradually ascending to the highest point. All points in thisline have an elevation of 0; all points on that line have an elevation of 1; all points onthat 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 theorange line out of the board at distance 2 in your mind's eye. That's the graph of thisfunction. It is a question of whether the graph of f, a function of x and y, is plane or curved.