SITE-C teams: Lesson 21

Consider the function f(x) = 3 x4 + 8 x3 - 6 x2 - 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 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 3 X^4 + 8 X^3 - 6 X2 - 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 (d2/dX2) 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).