SITE-C teams: Lesson 21

Consider the function f(x) = 3 x^{4} + 8 x^{3} - 6 x^{2} - 24 x + 10

What are the roots of this function? What are the local maximums, local minimums and inflection points of the function?

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 3 X^4 + 8 X^3 - 6 X^{2} - 24 X + 10 and press **EXE** to store it in memory.

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) to obtain the first root at x = 0.40119085694. Press the right cursor arrow once to obtain the second root at x = 1.4448006437.

Press **SHIFT F5** (G-Solv) **F2** (MAX) to obtain the only local maximum which is at ( -1, 23).

Press **SHIFT F5** (G-Solv) **F3** (MIN) to obtain the first local minimum which is at ( -2, 18). Press the right cursor arrow to obtain the second local minimum which is at ( 1, -9 ).

Press **EXIT** to return to the function list. Use the up or down cursor arrow to highlight Y1 and press **F1** (SEL) to de-select it.

An inflection point occurs where the second derivative of the function is zero.

Use the up or down cursor arrow to highlight Y2 and press the following:

**OPTN F2** (CALC) **F2** (d^{2}/dX^{2}) **VARS** **F4** (GRPH) **F1** (Y) **1, X ) EXE**.

The graph of the second derivative is displayed.

Press **SHIFT F5** (G-Solv) **F1** (ROOT) **EXE** to obtain the first inflection point which is at x = -1.545839843 (This calculation takes a little over 4 minutes.). Press the right cursor arrow to obtain the second inflection point at x = 0.21524963378 (Again this calculation takes over 4 minutes).

Press **EXIT** **MENU**.

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