Graphics Programs Reference
In-Depth Information
16
14
12
10
8
6
4
2
0
−
2
−
1.5
−
1
−
0.5
0
0.5
1
1.5
2
We see that there are points of intersection near
−
0.9 and 1.2. Are there any
other points of intersection? To the left of 0, 2
x
is always less than 1, whereas
x
4
goes to infinity as
x
goes to
−∞
. However, both
x
4
and 2
x
go to infinity as
x
goes to
∞
, so the graphs may cross again to the right of 6. Let's check.
X = 6:0.1:20; plot(X, 2.ˆX); hold on; plot(X, X.ˆ4, '--');
hold off
12
x 10
5
10
8
6
4
2
0
6
8
10
12
14
16
18
20
We see that they do cross again, near
x
=
16. If you know a little calculus,
you can show that the graphs never cross again (by taking logarithms, for
example), so we have found all the points of intersection. Now let's use
fzero
to find these points of intersection numerically. This command looks
for a solution near a given starting point. To find the three different points of
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