Information Technology Reference
In-Depth Information
5
x*
x=3
0
f(x)
−5
−10
−15
−20
0
0.5
1
1.5
2
2.5
3
3.5
x
e
x
Fig. 4.1
The graph of f.x/
D
2
C
x
We note that f.x
0
/
D
f.0/ > 0 and f.x
1
/
D
f.3/ < 0. Next, we define the mean
value
1
2
.x
0
C
x
1
/
D
3
2
:
x
2
D
(4.36)
Since we are looking for a point where f is zero, our next step thus depends on
the value of f.x
2
/. Obviously, if f.x
2
/ is zero, we just put x
D
x
2
, and our search
is completed. But f.x
2
/ is not zero. In fact,
f.x
2
/
D
f
3
2
D
2
C
3=2
e
3=2
<0;
(4.37)
see Fig.
4.2
.
Since f.x
0
/>0and f.x
2
/<0, we know that x
0
<x
<x
2
.Next,wedefine
1
2
.x
0
C
x
2
/
D
3
4
:
x
3
D