## Saturday, 16 August 2008

### Order Of An Equation

What is an order of an equation?

It is simply the highest power within the mathematical equation.

Example:

y = 3 x2 + 4x - 5 ==> This is a Second Order equation.

y = 2x3 - 6x2 + 6 ==> This is a Third Order equation.

Therefore the order is determined by the highest power in any term of the equation.

However, there is another interesting phenomenon of equations related to its quantity of maxima and minima points.

The maximum total number of maxima and minima points of an equation cannot be more than or equal to its Order.

A few graphs will illustrate this remark.

Second order equation produces only one turning point.

Third Order equation produces maximum 2 turning points (peak and dip).

Fourth Order equation produces a maximum of 3 turning points (peaks and dips).

From the above 3 graphs, we noticed that the order is always greater than the maximum total number of peaks and dips of that equation.

However, there is one point we should be aware.

The Order governs the maximum total number of maxima (peak) and minima (dip).
However, the actual total number can be less!

Example: Equation y = x4 produces only one turning point and not 3.

Finally, to conclude, can you guess what is the order for the below graph?