SITE-C teams: Lesson 19

Consider the following function: f(x) = x^{2} + 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

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 X^{2} + 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