BQ #7: Unit V- Difference Quotient

The Difference Quotient is something we've become very familiar with this year. But what we might not know is what it means and where is it derived from. Simply enough, the difference quotient formula is just the slope formula mixed around, more specifically the slope of all tangent lines.

http://cis.stvincent.edu/carlsond/ma109/diffquot.html

 

 

The slope formula is what? (y2-y1)/(x2-x1). If we refer to the points of f(x+h), F(x), and such, "h" representing the distance between the first point and the second. Our ordered pairs will be seen as (x, f(x)) and (x+h, f(x+h)). By plugging in both ordered pairs to the formula, the result would be f(x+h)-f(x)/x+h-x. When we cancel the x's we would get: f(x+h)-f(x)/h and VOILA the difference quotient!