SITE-C teams: Lesson 20

 

Consider the following function: f(x) = 5 x3 - 8 x2 + x - 2

What are the roots of this function? Where is the first derivative is 0?

Turn on the CASIO CFX-9850G by pressing AC/ON.

Use the cursor arrows to highlight the GRAPH menu and press EXE or just press 5 when at the main menu screen.

In the Y1 slot enter 5 X^3 - 8 X2 + X - 2 and press EXE to store it in memory.

Press SHIFT MENU (SETUP), use the down cursor arrow to scroll down and highlight the Derivative line, press F1 (On) EXIT.

Press SHIFT F3 (V-Window) to set the parameters as follows:

Xmin = -3.15

Ymin = -31

Xmax = 3.15

Ymax = 31

Xscale = 0.5

Yscale = 5

Press EXIT to return to the function list. Make sure that no other Y-slot is highlighted, i.e. selected for drawing. Press F6 (DRAW) to see the graph.

Press SHIFT F5 (G-Solv) F1 (ROOT). The only root is x = 1.6280643341.

The first derivative is zero at points where there is either a local maximum and minimum.

Press SHIFT F5 (G-Solv) F2 (MAX) to obtain the local maximum at ( 0.0666666746, -1.9674074074).

Press SHIFT F5 (G-Solv) F3 (MIN) to obtain the local minimum at ( 1, -4).

Press SHIFT F1 (Trace) and use the right cursor arrow to move to where dY / dX = 0. This point is ( 1, -4). The local maximum was bypassed by the Trace procedure.

To verify that the local maximum does have a zero first derivative, press SHIFT F2 (ZOOM) F1 (BOX) and use the cursor arrows to move to a point around the local maximum for the top left-hand corner of the box, say (0.05, -1) and press EXE. Use the cursor arrows to move to a point for the bottom right-hand corner of the box, say (0.1, -2) and press EXE.

Press SHIFT F1 (Trace) and use the right cursor arrow to move to where dY / dX = 0. This time the point ( 0.0666666666, -1.9674074074) appears thus verifying that the local maximum does have a zero first derivative.

Press EXIT MENU.

Turn off the CASIO CFX-9850G by pressing SHIFT AC/ON (OFF).