Loading ...
Loading ...
Loading ...
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)= 2x
3
– 7x
2
– 70x + 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
Loading ...
Loading ...
Loading ...