Question

How do you find the slope of a tangent line using secant lines?

Answer 1

The slope of a tangent line can be approximated by the slope of a secant line with one of the end point coincides with the point of tangency. So, if the slope of the secant line from a to a+h is

`{f(a+h)-f(a)}/{h}`,

then we can better approximate the slope of the tangent line by the slope of secant line by making `h` smaller and smaller. Hence, we can find the slope of the tangent line `m` at `x=a` by

`m=lim_{h to 0}{f(a+h)-f(a)}/{h}`