Page 13-8
Analyzing graphics of functions
In Chapter 11 we presented some functions that are available in the graphics
screen for analyzing graphics of functions of the form y = f(x). These functions
include (X,Y) and TRACE for determining points on the graph, as well as
functions in the ZOOM and FCN menu. The functions in the ZOOM menu
allow the user to zoom in into a graph to analyze it in more detail. These
functions are described in detail in Chapter 12. Within the functions of the
FCN menu, we can use the functions SLOPE, EXTR, F’, and TANL to determine
the slope of a tangent to the graph, the extrema (minima and maxima) of the
function, to plot the derivative, and to find the equation of the tangent line.
Try the following example for the function y = tan(x).
Θ Press „ô, simultaneously in RPN mode, to access to the PLOT
SETUP window.
Θ Change TYPE to FUNCTION, if needed, by using [@CHOOS].
Θ Press ˜ and type in the equation ‘TAN(X)’.
Θ Make sure the independent variable is set to ‘X’.
Θ Press L @@@OK@@@ to return to normal calculator display.
Θ Press „ò, simultaneously, to access the PLOT window
Θ Change H-VIEW range to –2 to 2, and V-VIEW range to –5 to 5.
Θ Press @ERASE @DRAW to plot the function in polar coordinates.
The resulting plot looks as follows:
Θ Notice that there are vertical lines that represent asymptotes. These are
not part of the graph, but show points where TAN(X) goes to ±∞ at
certain values of X.
Θ Press @TRACE @(X,Y)@, and move the cursor to the point X: 1.08E0, Y:
1.86E0. Next, press L@)@FCN@ @SLOPE. The result is Slope:
4.45010547846.
Θ Press LL@TANL. This operation produces the equation of the
tangent line, and plots its graph in the same figure. The result is shown
in the figure below:
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