Finding the Max and Min of a Function
Kevin Fitzpatrick • CC Edwards
CALCULATORS: Casio: fx-9750G Plus & cfx-9850G Series
TI: TI-83 Plus, TI-84 Plus & TI-83/TI-84 Plus Silver Editions
CASIO GRAPHING CALCULATORS
TI GRAPHING CALCULATORS
Finding max and min values on the Home screen
of: f(x)= 9x4 + 2x3 –3x2
Finding max and min values on the Home screen
of: f(x)= 9x4 + 2x3 –3x2
From the graph shown below, it appears that
f(x)= 9x4 + 2x3 –3x2 has an absolute minimum in
[-1,0], an obvious relative maximum at x = 0, and a
relative minimum in [0, 1].
From the graph shown below, it appears that
f(x)= 9x4 + 2x3 –3x2 has an absolute minimum in
[-1,0], an obvious relative maximum at x = 0, and a
relative minimum in [0, 1].
To find the absolute minimum:
To find the absolute minimum:
1. Press MENU then 1 (RUN) to select the main
calculation HOME screen.
1. Enter the function in the Y= editor.
2. Press MATH 6 to select fMin from the
MATH/MATH menu.
3. Enter the function and then press , . If the
function is stored in the Y= editor, press VARS
right arrow and ENTER. Then press the
number key corresponding to the number of the
function in the Y= editor.
2. Press OPTN, then F4 (CALC), then F6 to move
ahead one screen, then F1 (FMin). This will
place the FMin command on the screen.
4. Enter the letter of the function variable (x) and
press , .
5. Enter the lower limit of the interval containing
the minimum, press , then enter the upper limit,
and press ) .
6. Press ENTER to find the absolute minimum in
that interval.
The calculator gives you the location (x-value)
of the absolute minimum, as shown in the
second line of the above screen shot.
Finding the Max and Min of a Function
1
© Casio, Inc. • For Classroom Use Only
Finding the Max and Min of a Function
continued
CALCULATORS: Casio: fx-9750G Plus & cfx-9850G Series
TI: TI-83 Plus, TI-84 Plus & TI-83/TI-84 Plus Silver Editions
CASIO GRAPHING CALCULATORS
TI GRAPHING CALCULATORS
The third line of this screen shot shows that you
can evaluate the y-value of this minimum by
entering the function and pressing 2nd ANS to
enter the x-value of this minimum.
3. Into the FMin command: Enter the function, the
lower bound and the upper bound and press
EXE.
The relative minimum in [0, 1] can be found by
further restricting the limits of the interval, as
illustrated in the fourth line as shown in the
screen shot.
4. Both the x and y-values of the minimum point
will be displayed on a second screen in a matrix
format.
The maximum value is found in a similar
manner by pressing fMax to select fMax from
the MATH/MATH menu.
5. The relative minimum in [0, -1] can be found by
further restricting the limits of the interval, as
illustrated in the above screen shot.
6. The maximum value is found in a similar
manner by pressing OPTN, then F4 (CALC),
then F6 to move ahead one screen, then F2
(FMax).
Finding the Max and Min of a Function
2
© Casio, Inc. • For Classroom Use Only
Finding the Max and Min of a Function
continued
CALCULATORS: Casio: fx-9750G Plus & cfx-9850G Series
TI: TI-83 Plus, TI-84 Plus & TI-83/TI-84 Plus Silver Editions
CASIO GRAPHING CALCULATORS
TI GRAPHING CALCULATORS
Finding max and min values on the Graph screen
of: f(x)= 9x4 + 2x3 –3x2
Finding max and min values on the Graph screen
of: f(x)= 9x4 + 2x3 –3x2
After graphing the function, follow these steps:
• To find the minimum(s), press F5(G-Solve), then
F3 (MIN). It will locate the minimum starting at
the left most, and show the point and coordinates
on the screen. To find subsequent minimum
points, press the right arrow. (User note:
watch the screen, the cursor will visibly "walk"
to the next value.
After graphing the function, follow these steps:
1. Press 2nd CALC to access the
GRAPH/CALC menu. Press 3 to find a
minimum or press 4 to find a maximum.
•
2. Enter the lower limit of the interval containing
the minimum and press ENTER .
3. Enter the upper limit of the interval containing
the minimum and press ENTER .
To find the maximum(s). Repeat the process
above, using F2 (MAX). User note: No need to
guess at values or place the cursor. It will begin
at the left, find the values, display the function,
graph, point, and a Max or Min screen note.
4. When prompted for a guess, enter a number near
the location of the x-coordinate of minimum or
maximum.
5. Press ENTER to find the absolute minimum or
maximum. If there are two absolute minimums
(or maximums) in the interval, the calculator
will find the absolute minimum (maximum)
closest to your guess.
THE CASIO ADVANTAGE
•
•
•
•
•
Same functionality
Greater efficiency, much fewer keystrokes
Move more directly to the desired result
No danger of capturing a value that is not
desired
The fx-9750G Plus costs approximately 1/2 the
price of the TI-83 plus.
Finding the Max and Min of a Function
3
© Casio, Inc. • For Classroom Use Only