ANTIDERIVATIVE GRAPHS
Objective: Plot an antiderivative graph of a given function and make connections
between the antiderivative graph and the function graph.
Use your graphics calculator to sketch the antiderivative graph of these functions:
1. y = 0.5( x + 2)( x − 3)
x
2. y = 2 cos 2 ( )
2
3
3. y = x − 2 x 2 + x − 1
sin( x)
4. y =
x
5. y = 200 x × 2 − x
For each graph plot the graph of the function and of an antiderivative function on one
set of axes. Hence describe any relationships you can find between the two graphs.
Summarise your findings in the table below:
Function f ( x)
Antiderivative function F ( x)
Crosses the x-axis from negative to
positive
Crosses the x-axis from positive to
negative
Has a turning point not touching the xaxis
Has a turning point touching the x-axis
Has a stationary point of inflexion
©Bozenna Graham 2009
[email protected] 1
Graph 1
To sketch the antiderivative graph we use
nInt, which can be found in Catalogue.
The standard Window was used for the
graphs below:
Notice that f2(x) has a dotted line to
distinguish easily between the two
graphs. Select it from Attributes (rightclick).
What happens to the antiderivative graph
when we change
f 2( x) = fnInt ( f 1( x), x,1, x)?
Graph 2 (MODE: Radians)
©Bozenna Graham 2009
Graph 3
[email protected] 2
Graph 4
Graph 5
After you have filled in the table above you should be able to deduce the graph of the
antiderivative function, given the graph of the original function.
Try this one now: On the same set of axes draw a graph of the antideriative function:
y
4
3
2
1
-1
-1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
x
Discuss your solution with another person in the classroom.
The function depicted above have the following rule:
6
f ( x) = − 6 + 3log e ( x)
(VCAA 2000 Exam 2).
x
Check the graph you drew with the one on your
graphics calculator. Correct any mistakes you may
have.
©Bozenna Graham 2009
[email protected] 3