Graphs with Mathematica

The derivative    in one variable is related to the graph    by giving the slope of the line tangent to the graph.

There are two main plots of a function  : explicit and contour plots.  You can make them easily with Mathematica as follows.  In the tour below we will show you how Mathematica helps you understand the relationship between the total derivative and tangency to explicit, implicit, and parametric graphs in several variables.

Mathematica even helps understand basic plotting.  For example, we can make surface plots by hand if we fix the value of one input variable, say    and plot this 2D curve in the plane  , then vary the constant.  This is tedious, but two dimensional.  The next figure shows how this looks and it is animated as the slicing plane moves.  Click the link below the graph to see the animation.

Load the Animation