The TI-89 has a perfectly nice built-in tangent-line function accessed through the Menu on the graph screen. Suppose that we want to find an equation of the tangent line to the graph of y = 3x2 - ln x at the point (1, 3) (This is problem #67 on p. 319 of the Larsen text.) A graph of this function is shown at right using the window . |
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Select "A: Tangent" from the menu. |
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You can either use the arrow keys to select a point on the graph, then press , or type an x-coordinate and press in answer to the "Tangent at?" question. |
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The equation of the tangent line is given as "y = 5.x - 2.". The decimal points indicate that this is an approximate answer (although in this case it happens to be exact). |
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To get an exact answer to the question "What is an equation of the tangent line..." you can enter a new function. It is:
Define tanline(f, x, c) = (d(f, x) | x = c)*(x - c) + (f | x = c)
The screen shot at right shows the result of using the tanline() function to solve the same problem as above. An advantage of this function over the "A: Tangent" method is that the user-defined function can produce exact results. |
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