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