Expression 9: "x" Subscript, 2 , Baseline equals "x" Subscript, 1 , Baseline minus StartFraction, "f" left parenthesis, "x" Subscript, 1 , Baseline , right parenthesis Over "f" prime left parenthesis, "x" Subscript, 1 , Baseline , right parenthesis , EndFractionx2=x1−fx1f′x1
equals=
negative 1.7 5 3 8 4 6 1 5 3 8 5−1.75384615385
9
Expression 10: "x" Subscript, 3 , Baseline equals "x" Subscript, 2 , Baseline minus StartFraction, "f" left parenthesis, "x" Subscript, 2 , Baseline , right parenthesis Over "f" prime left parenthesis, "x" Subscript, 2 , Baseline , right parenthesis , EndFractionx3=x2−fx2f′x2
equals=
negative 1.9 5 9 3 9 7 3 0 3 7 3−1.95939730373
10
Expression 11: "x" Subscript, 4 , Baseline equals "x" Subscript, 3 , Baseline minus StartFraction, "f" left parenthesis, "x" Subscript, 3 , Baseline , right parenthesis Over "f" prime left parenthesis, "x" Subscript, 3 , Baseline , right parenthesis , EndFractionx4=x3−fx3f′x3
equals=
negative 1.9 9 8 4 7 5 2 3 9 8 1−1.99847523981
11
Expression 12: StartRoot, 3 , EndRoot3
equals=
1.7 3 2 0 5 0 8 0 7 5 71.73205080757
12
Below you can see the construction of each tangent line, which is the function we set equal to 0 at each stage to solve for the next guess.
