I just want to show off how smart I am
Proof of the post I made earlier:
By taking the first derivative of a function of degree zero or one with respect to the whichever value the function is evaluated at (usually x or t) you get either constant value. For a function of degree zero you get zero. For a function of degree one, you get the slope of the straight line. Because this is constant, the slope of the function at any value of the variable is the same, so the graph of the function rises (or falls) at the same rate.
For a function of a degree above one or below zero however, the first derivative is going to be either a function of degree one or higher, a function of a negative degree, or a natural logarithm (the case if the degree of the original function was -1) Because of this, the slope of the original function is going to vary as the value of the abscissa changes so the graph is going to curve.
Quod Erat Demonstrandum
(I won't bother going into any trig functions or any other non-algebraic stuff)
[Edited by Ziggy2 Stardust on 11-18-2000 at 21:02]