Explain in detail where the formula for the difference quotient comes from now that you know! Include all appropriate terminology (secant line, tangent line, h/delta, x, etc).
In the picture above we have drawn a parabola with a secant line intersecting the parabola at two different points. The points are labelled (f(x),x) and (f(x+h),x+h), where 'h' is the distance between the points. In order to find the slope of the secant line we use the equation: Y2-Y1/X2-X1. The equation turns into the difference quotient equation: f(x+h) - f(x)/x+h - x = f(x+h) - f(x)/h.
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