**Tangent Line**

The Casio can draw the tangent line to a curve at a point and also display the equation of the tangent line to a function at a point. However, these are done in different menu screens.

**Draw a Tangent Line**

From the graph screen we can draw the equation of a tangent line to a specified point on the graph of a function. For illustration, we draw the tangent line to the function

y= -.2x^{3}- (x- 1)^{2}+ 4

at
x = 1. First, enter the function into the equation editor: press **MENU
F6** to access the GRPH-TBL screen, enter the function as Y1, then press **F5**
to select DRAW. The graph view in the screen pictured above is seen in the standard
viewing window: press **SHIFT V-Window**, press
**F3** to select STD, press **EXE** to return
to the equation editor, and finally press **F6** to select DRAW and see the
graph in the standard viewing window.

From the graph screen, press **F3** to access the SKTCH menu. Either press
**6** to select 6: Tangent, or scroll up the G-SLV menu to highlight **6:Tangent**
and then press **EXE**. The screen displays the
graph with a cross prompting you for the *x*-coordinate of the point at which
you want the tangent. Enter the *x*-value at which you want the tangent line.
Here, *x* = 1, so press **1** **EXE**.
An Enter X-Value pop-up screen appears. When the correct X value is displayed,
press **EXE**. The appropriate point is then marked.
Press **EXE** again and the tangent line is drawn.
The coordinates of the marked point are displayed at the bottom of the screen.

**Equation of a Tangent Line**

Once we have drawn the tangent line to a function at a point, we’d like
to know the equation of that tangent line. Press **ESC** to return to the equation
editor. We now save the function so we won’t have to enter it again. Press
**F4** to select GMEM, then press **1** to select 1:Store. You can store
up to 20 functions in memory. Press **1 EXE**
to save the function as Y1.

Press
**MENU 9** to access the CAS screen. Press **F2**
to access the CALC menu. Either press **8** to select 8:tanLin, or scroll up
the CALC menu to highlight 8:tanLin and then press **EXE**.
The expression tanLine( is then pasted into the entry line. Use the syntax

tanLine(function, variable, x-value)

to find the equation of the tangent line. Because we have saved the function as Y1, simply press

**VARS
F1 1 , X , 1 ) EXE**

Hence, the equation of the tangent line to

*y* = -.2*x** *^{3} - (*x* - 1)^{2} + 4 at
x = 1 is *y* = -3*x*/5 + 22/5.