Ah, you're moving into the general case of numerical analysis -- that is, to sample finite points of a (hopefully!) well-behaved function, and how to do it in a reasonable way, and also a stable way, while achieving some purpose (usually differentiation or integration).
You want good confidence that you aren't missing points, without taking a wasteful number of points in the process. Too few points, or too naive a method, and you will find unlucky combinations spiraling out of control -- see Newton's method of root finding for a fairly simple case.
In this case, you're not so much after differentiation or integration, as just plotting the function at all. But doing that is governed by the same arguments, so study of these subjects should be quite fruitful indeed.
Tim