A. Bisection B. False position C. Newton-Raphson

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Below is a list of all of the root-finding methods discussed in class. For each scenario below, first list all methods from the list that could be used to find the root shown (listing letters is fine – no need to spell out the names).

A. Bisection
B. False position
C. Newton-Raphson
D. Traditional secant
E. Modified secant
F. Inverse quadratic interpolation
G. fzero (in MATLAB)
H. roots (in MATLAB)

 

a. Scenario 1: y = 3(x – 1)²
b. Scenario 2: y = tan x
y
3.5
15.0
3.0
y = tan x
10.0
Root at x = 0
2.5
y = 3(x – 1)²
5.0
Roots at x = 1
2.0
1.5
-1.5
-0.5
0.5
1.5
-5.0
1.0
-10.0
0.5
0.0
-15.0
0.5
1
1.5
2
Transcribed Image Text:a. Scenario 1: y = 3(x – 1)² b. Scenario 2: y = tan x y 3.5 15.0 3.0 y = tan x 10.0 Root at x = 0 2.5 y = 3(x – 1)² 5.0 Roots at x = 1 2.0 1.5 -1.5 -0.5 0.5 1.5 -5.0 1.0 -10.0 0.5 0.0 -15.0 0.5 1 1.5 2
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