Comments from a Ph.D. in mathematics.

A five star grapher MUST have the following:
1. The ability to do multiple functions in different colors at the same time.
2. The ability to find inflection points, axis intercepts, maxima & minima, and intersections of curves.
3. The ability to graph implicit functions like x^2 + y^2 = 4
4. The ability to graph the derivative and definite integral between any two points.
5. A function type keyboard for convenience of entering equations.

This has the first three done better than any I have seen. If they add the last two, it will clearly be the very best grapher available for the iphone!

HMWhitcraft about Graphicus - Graphing Calculator