Chapter 8: Numerical Methods
Locating roots
Roots: A root of a function is the value of x for which f (x) = 0:
In other words, the point where the functioncrosses the x-axis.
numbers
If the function f(x) is continuous on the interval [a, b] and f(a) and f(b) have
opposite signs, then f(x) has at least one root in the interval (a,b).
Steps
1. Rewrite the equation into the form f (x) = 0:
2. Evaluate f(a) and f(b) and check their signs.
Feast
3. If f(x) changes its sign, then there is a root between the interval (a, b)
one not
pyo 8
I i
81b gas gib
feb
Example 1:
813
a thegraphcrosses thex axis g
I
between 2 and 3
8127 0 813370
b 14 1.413 4 1.412 321.4 1 0.104 fct
f 1.573 461.532 3 1 5 1 0.125 gu
8115
i there is a
changeof sign between 14,91,5
Locating roots
Roots: A root of a function is the value of x for which f (x) = 0:
In other words, the point where the functioncrosses the x-axis.
numbers
If the function f(x) is continuous on the interval [a, b] and f(a) and f(b) have
opposite signs, then f(x) has at least one root in the interval (a,b).
Steps
1. Rewrite the equation into the form f (x) = 0:
2. Evaluate f(a) and f(b) and check their signs.
Feast
3. If f(x) changes its sign, then there is a root between the interval (a, b)
one not
pyo 8
I i
81b gas gib
feb
Example 1:
813
a thegraphcrosses thex axis g
I
between 2 and 3
8127 0 813370
b 14 1.413 4 1.412 321.4 1 0.104 fct
f 1.573 461.532 3 1 5 1 0.125 gu
8115
i there is a
changeof sign between 14,91,5
