Using The Second Derivative - Casio fx-9860GII Instructions Manual

Press to select the second point.
The GDC shows a point of intersection at (2, 3).
The curve has gradient 3 when x = –4 and x = 2.

2.6 Using the second derivative

The calculator can fi nd fi rst and second derivatives. The second derivative
can be used to determine whether a point is a maximum or minimum point.
Example 35
Find the stationary points on the curve f (x) = x
f (x) = x 4 − 4x 3
f '(x) = 4x
3 − 12x 2
At stationary points
f '(x) = 0
3 2
4x − 12x = 0
2
4x (x − 3) = 0
Therefore x = 0 or x = 3.
MENU
Press . You will see the dialog box as shown on the right.
Choose 5: GRAPH and press
4 3
Enter x − 4x for Y1.
MENU
Press . You will see the dialog box as shown on the right.
Choose 1: RUN·MAT and press
Use the calculator to fi nd the coordinates of the points and to
determine their nature.
Evaluate the function when x = 0 and x = 3.
Press | GRPH |
VARS F4
Similarly enter Y1(3).
The stationary points are at (0, 0) and (3, −27).
© Oxford University Press 2012: this may be reproduced for class use solely for the purchaser's institute
4
− 4x
EXE .
EXE
.
Use
Press
line.
Y then type 1(0)l to enter Y1(0).
F1
3
and determine their nature.
to enter the exponent.
to return to the base
Casio fx-9860GII
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Continued on next page
Using a graphic display calculator 34