The difference formula is the slope of a line, which is also known as a secant of a graph. The original slope formula is (y2-y1)/(x2-x1) and we derive the difference formula from this. The two points that we use to plug in are (x, f(x)) and (x+h, f(x+h)). "H" represent the change in x and is also referred to as delta x. Then we would plug in those two coordinates and get f(x+h)-f(x) over (x+h)-x which we need to simplify. The x and -x cancel, so we would get f(x+h)-f(x)/h which is ultimately the difference formula derived from the slope formula.
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| http://cis.stvincent.edu/carlsond/ma109/diffquot.html |
