Information accurate for OS 3.06.1000.
If information is known about a function and/or its derivative, and the function contains unknown co-efficients, then that information can be used to determine the value of the unknown co-efficients.
In the example below, it is known that the quadratic function defined as f(x) has a turning point at (3,9). If we define g(x) as the derivative of f(x) then we have two equations, f(3)=9 and g(3)=0, and two unknowns, a and b. If we tap ~ then these equations can be entered, and the unknowns can be solved for, as shown.
NOTE: OVER-SPECIFIED SYSTEMS OF EQUATIONS.
If the number of equations exceeds the number of unknowns then the system of equations can still be solved, assuming that the equations are consistant.