With the formula for the derivative of
the derivative can be used to find slopes of tangent lines to the graph
of the function f(x)=ex.
At a point (x0,y0) on the
graph of f(x)
(so that y0=f(x0)),
the line tangent to the graph will have slope
m=f '(x0). Plugging into the
Point-Slope form equation for a line, then, the equation for the tangent
line at (x0,y0) will be:
This is the equation used to find the tangent lines to the graph in the
applet below. Using the functions
f '(x)=ex, the applet shows the
tangent line for any given value of x0 in the graph, starting
below with x0=1.
How to use this applet
Other values for x0 (shown in the
"x=" field in the applet) can be chosen either
by entering a new value into the "x=" field
or by clicking and dragging the mouse on the graph.