SITE-C teams: Lesson 20

Consider the following function: f(x) = 5 x^{3} - 8 x^{2} + x - 2

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

Turn on the **CASIO CFX-9850G** by pressing

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 X^{2} + 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