SITE-C teams: Lesson 19

 

Consider the following function: f(x) = x2 + 5 x - 3

What are the roots of this function? Where is the first derivative is 0? Draw the graph of this function and draw the line with slope 5 that is tangent to f(x). What is the equation for the tangent line at that point?

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 X2 + 5 X - 3 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 = -6.3

Ymin = -62

Xmax = 6.3

Ymax = 62

Xscale = 1

Yscale = 10

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 first root is x = -5.5413812651. Press the right cursor arrow to obtain the second root. It is x = 0.54138126514.

Press SHIFT F1 (Trace) and use the right cursor arrow to move to where dY / dX = 0. The point at which the first derivative of the function is zero is ( -2.5, -9.25).

Use the right cursor arrow to move to the point where dY / dX = 5. This point is ( 0, -3 ). Since the slope of the tangent line at that point is 5 and the line passes through the point ( 0, -3 ), then the equation for the tangent line is y + 3 = 5 x, or y = 5 x - 3.

Press EXIT to return to the function list. Enter into the Y2 slot 5 X - 3 and press EXE to store it in memory. Use the up cursor arrow to highlight Y2, press F4 (COLR) F2 (Orng) EXIT.

Press F6 (DRAW) to see f(x) and the tangent line with slope 5.

To verify press SHIFT F4 (Sketch) F2 (Tang), use the right cursor arrow to move to ( 0, -3 ), and press EXE to draw the tangent line at that point. Nothing new is displayed indicating that the tangent line is displayed.

Press EXIT MENU.

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