Two Points Determine a Secant
The line between the two points on
f(x) is called a Secant Line of the function f(x). Geogebra has automatically named this secant line g. The slope of g is currently 4.1.
Adjust h with its slider.
- Notice that as
hgets close to zero, the secant line almost perfectly matches the functionf(x)at pointA. - When
his exactly 0, the line disappears because two unique points are needed to determine a line. - Pay close attention to the slope of the secant line when
hlimits toward 0. Can you detect a trend?
(h, slope(g))Move to the next activity for an explanation.