Enter a function f (x) in the text input field
marked "f (x)="
(Example:f (x) = x2)
Click the "Graph" button
(this button also refreshes the graph)
Enter the derivative f '(x)
in the text input field
marked "f '(x)="
(Example:f '(x)=2x)
Select values for x1, x2,
and c
(Example:x1=0, x2=1,
c=0.5)
This can be done in either of two ways:
Use the mouse to click and drag the
red points on the graph --
the points follow the graph of f (x), and the
values of x1 and x2
correspond to the horizontal positions of the points on graph
Enter the values in the text input fields marked
"x1=",
"x2=", and
"c=",
and click the
"Graph" button to refresh
To erase the graph and all input fields (setting
x1, x2,
and c to default values), click the
"Clear" button
The text input field marked "f (x)=" can accept
a wide variety of expressions to represent functions.
The text input fields marked
"x1=",
"x2=", and
"c="
can accept a real number in decimal
notation. The
buttons under the graph
allow various manipulations of
the graph coordinates.
Exponential: f (x) = ex f '(x) = ex x1=-1, x2=1 c=0.161439
Other Notes
The graph shows a secant line for f (x) through
the points (x1,f (x1))
and (x2,f (x2)),
and a tangent line through the point
(c,f (c)).
Labels with the text input fields also show the values of
f (x1), f (x2),
the slope of the secant line, and f (c).
The Mean Value Theorem states that, as long
as f '(x) is continuous, there must be a value of c
between x1 and x2
for which the secant line and the
tangent line are parallel. This applet allows the user to experiment
with the secant line and tangent line, attempting to find such a value
for c.