Homework Problems for Regula-Falsi Method.
1.
Find each of the following for the function f x   x 4  5x  2 .
a. Explain why f x  must have a root on the interval 0,1 and a second root on the interval 1,2 .
b. Apply two iterations of the Regula-Falsi Method to estimate the root on the interval 0,1 .
iteration
a
b
xrfp
f(a)
f(b)
1
0
f(xrfp)
1
2
c. Apply two iterations of the Regula-Falsi Method to estimate the root on the interval 1,2 .
iteration
a
b
xrfp
f(a)
f(b)
1
1
f(xrfp)
2
2
2.
3.
If the interval 0,2 is used as the initial interval for the function f x  in question (1) which of the two
roots on this interval will the Regula-Falsi method find. Explain.
A function f x  is pictured to the right.
a. Draw the graph and locate on the x-axis
the next two Regula-Falsi estimates (i.e.
xrfp) call them e1 and e2 .
b. Estimate the values for e1 and e2 .
c. Estimate the value of the root.
4
2
0
0.2
2
4
0.4
0.6
0.8
1.0
1.2
1.4