Secant line representing the slope of a tangent?

[kendang]

How can a secant line be used to represent the slope of a tangent on a polynomial function y=f(x)?

I can't remember how to precisely explain the solution. It had to do with "instantaneous rate of change" of the tangent and "average rate of change" of the secant point from A to B. Can someone please clarify this subject? Thanks!

 

[Deleted member 4993]

How can a secant line be used to represent the slope of a tangent on a polynomial function y=f(x)?

I can't remember how to precisely explain the solution. It had to do with "instantaneous rate of change" of the tangent and "average rate of change" of the secant point from A to B. Can someone please clarify this subject? Thanks!

\(\displaystyle \left [\frac{df(x)}{dx}\right ]_b \ = \ \lim_{a\to b}\left [\frac{f(b)-f(a)}{b-a}\right ]\)

In the above expression - do you recognize the slope of the secant line?