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1. Plot the particular function over the defined domain.
2. Examine the plot to determine whether the extremum is an end-
point extremum or a local extremum.
3. Zoom in on the neighborhood of the so-identified extremum by
repeated application of the MATLAB axis or zoom commands.
4. Use the cross hair of the ginput command to read the coordinates
of the extremum. [Be especially careful here. Extra caution is
prompted by the fact that the curve is flat (its tangent is parallel
to the x-axis) at a local extremum; thus, you may need to re-plot
the curve in the neighborhood of this extremum to find, through
visual means, accurate results for the coordinates of the extremum.
There may be too few points in the original plot for the zooming
technique to provide more than a very rough approximation.]

In-Class Exercises
Find, graphically, for each of the following exercises, the coordinates of the
global maximum and the global minimum for the following curves in the
indicated intervals. Specify the nature of the extremum.

2
Pb. 5.17 y = f(x) = exp(–x ) on –4 < x < 4
2
2
Pb. 5.18 y = f(x) = exp(–x ) sin (x) on –4 < x < 4
2
3
Pb. 5.19 y = f(x) = exp(–x ) [x + 2x + 3] on –4 < x < 4
Pb. 5.20 y = f(x) = 2 sin(x) – x on 0 < x < 2π

Pb. 5.21 y = f x =( ) 1 + sin( x) on 0 < x < 2π

5.3.2 Numerical Methods

We discuss now the Golden Section method for evaluating the position of the
local minimum of a function and its value at this minimum. We assume that
we have plotted the function and have established that such a local minimum
exists. Our goal at this point is to accurately pinpoint the position and value
of this minimum. We detail the derivation of an elementary technique for this
search: the Golden Section method. More accurate and efficient techniques
for this task have been developed. These are incorporated in the built-in com-
mand fmin; the mode of use is discussed in Section 5.3.3.

© 2001 by CRC Press LLC