Response to grace's post----

The difference quotient formula is used to find a function's derivative, which is like the slope of a point (yeah that doesn't seem possible) but i think its like the slope of the point's tangent, so if the f(x) is x^2-2, and after using the difference quotient, u get 2x or something, u plug in an x value and use that to find the slope of that x value. However, if one sets the result f the difference quotient = to zero, the resulting x value is the optimization of the problem, so to combine optimization and difference quotient, i would say u could find the f(x) to use in the difference quotient by using the optimization methods, plug that into the difference quotient formula, and then set it to zero, resulting in the optimized x - value..... (setting it equal to zero comes from the idea that the derivative = the slope at one point, so if the slope is 0, the point must be at a max or turning point)..... also-- the difference quotient is: [f(x+h) - f(x)]/h Isaac Newton used this notation when finding the derivative, and what it means is that the slope of a certain graph chunk (the formula is slope if u noticed) even if its a curve, when the chunk is sent to an infinitesimally small space (this is done when one stipulates h->0) this may define a point.