TI89 MiniTutorial

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TI-89 Mini-Tutorial

• Tangent Lines

The purpose of the mini-tutorials is to
demonstrate the capabilities of the TI-89s
built-in computer algebra system (CAS). This
presentation in particular focuses on finding and
graphing tangent lines to a function.
Before you start this tutorial, you should
execute the NewProb command under the Clean Up
tab to clear a through z, turn off all graphs,
and clear your Home screen.
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Just as there are multiple ways to calculate
derivatives, there are several techniques for
finding tangent lines to other functions. This
presentation will feature the Tangent tool found
on the Graph screen under the Math menu tab.

• While this method is the quickest and best for
  checking work or exploring graph behavior, it
  does have two disadvantages of which you need to
  be aware
• The generated tangent line graph is a drawing,
  not a graphed function, so you cannot trace
  values on it. Regraphing anything will cause it
  to disappear.
• The generated tangent line equation is not
  saved and will disappear once you leave the Graph
  screen.

Another method will be shown at the end of this
presentation using techniques from previous
mini-tutorials. It takes longer, but avoids the
disadvantages above.
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Here are the steps to generating the tangent line
as a drawing

• Graph the function to which the line will be
  tangent (make sure the point of tangency is in
  the viewing window).
• Press F5 for the Math menu tab and select
  ATangent.
• Type the x-coordinate for the point of tangency
  and press ENTER.

• Lets look at a specific example, the tangent
  line to y x3 4 at x 1.
• From the Y screen, define and graph
  y1(x)x3-4.
• Select ATangent from the Math menu.
• Type 1 and press ENTER.

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Another method for finding the tangent line
involves the use of the d( ) command and the
techniques of defining variables and functions.

• From the Y screen, store the original function
  as y1(x).
• From the Home screen, use d( ) to calculate the
  numerical derivative at the point of tangency,
  then store that value as m.
• Define y2(x) as m(x-a)y1(a), where a is
  the x-coordinate of the point of tangency.

Make sure you type m(x-a) and not m(x-a).
The latter will cause the CAS to look for a
function named m, so the multiplication symbol
must be included here.
With this method, any typical graphing tool can
also be used on the tangent line. Lets look at
the same example from before, but using this
technique.
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TI-89 Mini-Tutorial

• Tangent Lines

This concludes the presentation on finding and
graphing tangent lines to a function.
Details and additional information can be found
in the TI-89 manual. Click here to download a
PDF version of it.