Fun with Math!: Secant & Tangent

Friday, May 20, 2011

Secant & Tangent

The graph below shows the process of getting instantaneous rate of change (slope of tangent) from average rate of change (slope of secant).

The red curve is given as y = g(x). Take note that the average rate of change of y from point A to point B is
$m_s=\frac{y_2 - y_1}{x_2 - x_1}=\frac{\Delta y}{\Delta x}$ .
Drag point B to observe the change of the slope of secant line, m_s. As point B is getting nearer to point A, the value of the slope of secant line is approaching to the value of the slope of tangent line at point A, m_t.
$m_t=\lim_{\Delta x\rightarrow 0} m_s=\lim_{\Delta x\rightarrow 0} \frac{\Delta y}{\Delta x}$

Betty, Created with GeoGebra

Fun with Math!

Pages

Friday, May 20, 2011

Secant & Tangent

No comments:

Post a Comment