Sharp EL-9900 EL9900 Operation Manual - Page 83

Graphs Of Derivatives

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GRAPHS OF DERIVATIVES 1. Graph f '(x) by pressing Y= ENTER entering f(x)= 2x3 - 7x2 - 70x + 75 for d Y1, and entering dx (Y1) for Y2. Enter Y2 by pressing MATH A (CALC) 0 5 (d/dx() 2ndF VARS ENTER A (XY) 1 (Y1) and press ) ENTER . 2. Press WINDOW (-) 1 0 ENTER 1 0 ENTER 1 ENTER ZOOM A (Zoom) 1 (Auto) to obtain the graphs of f(x) and f '(x). 3. We now want to find the two x-intercepts of f '(x). Press TRACE ▼ to place the tracer on the graph of the derivative. Then, press 2ndF CALC and 5 (X_Incpt). Press 2ndF CALC 5 (X_Incpt) again to obtain the other x-intercept. 4. Comparing these values to the x-coordinates of the points at which the maxima and minima of f(x) occur, we see they are the same. 5. Where is f '(x) positive? Notice this is where the graph of f(x) is increasing. Where is f '(x) negative? Notice this is where f(x) is decreasing. 6. Next, find the minimum point of f '(x) by first making sure the trace cursor is on the graph of the derivative, pressing 2ndF CALC 3 (Minimum). 7. Look at f(x) and observe that this appears to be the point at which the function "bends a different way." 8. Find the point of inflection directly by moving the cursor to the original function and pressing 2ndF CALC 7 (Inflec). 8 Advanced Keyboard/CALCULUS USING THE SHARP EL-9900 Copyright © 2002, Sharp Electronics Corporation. Permission is granted to photocopy for educational use only.

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8
Advanced Keyboard/CALCULUS USING THE SHARP EL-9900
Copyright © 2002, Sharp Electronics Corporation.
Permission is granted to photocopy for educational use only.
1.
Graph
f
’(
x
) by pressing
Y=
ENTER
entering
f
(
x
)= 2
x
3
– 7
x
2
– 70
x
+ 75 for
Y1, and entering
(Y1) for Y2.
Enter Y2 by pressing
MATH
A
(CALC)
0
5
(d/dx
(
)
2ndF
VARS
ENTER
A
(XY)
1
(Y1)
and press
)
ENTER
.
2.
Press WINDOW
(–)
1
0 ENTER
1
0
ENTER
1
ENTER
ZOOM
A
(Zoom)
1
(Auto) to obtain the graphs of
f
(
x
) and
f
’(
x
).
3.
We now want to find the two
x
-intercepts of
f
’(
x
).
Press
TRACE
▼
to
place the tracer on the graph of the derivative.
Then, press
2ndF
CALC
and
5
(X_Incpt)
. Press
2ndF
CALC
5
(X_Incpt)
again to obtain the
other
x
-intercept.
4.
Comparing these values to the
x
-coordinates of the points at which the
maxima and minima of
f
(
x
) occur, we see they are the same.
5.
Where is
f
’(
x
) positive?
Notice this is where the graph of
f
(
x
) is increasing.
Where is
f
’(
x
) negative?
Notice this is where
f
(
x
) is decreasing.
6.
Next, find the minimum point of
f
’(
x
) by first making sure the trace cursor is
on the graph of the derivative, pressing
2ndF
CALC
3
(Minimum)
.
7.
Look at
f
(
x
) and observe that this appears to be the point at which the
function “bends a different way.”
8.
Find the point of inflection directly by moving the cursor to the original
function and pressing
2ndF
CALC
7
(Inflec)
.
GRAPHS OF DERIVATIVES
d
dx