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

Sep 20, 2014

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

$\frac{f \left(a + h\right) - f \left(a\right)}{h}$,

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

$m = {\lim}_{h \to 0} \frac{f \left(a + h\right) - f \left(a\right)}{h}$