Question

What is the best reason one might want to use the Secant method instead of Newton’s method (for solving f(x) = 0)? (

Circle the TWO most correct answers.)

i. It is always guaranteed to converge, while Newton’s method is not.

ii. The Secant method can be used without having a formula for f′(x).

iii. Newton’s method exhibits faster convergence than the Secant method.

Answer #1

Suppose we want to apply Newton’s method to solving f(x) =
0where f is such that |f′′(x)| <10 and |f′(x)|> 2 for all x.
How close must x0 be to τ for the method to converge?

Suppose we want to apply Newton’s method to solving f(x) =
0where f is such that |f′′(x)| < 10 and |f′(x)| >2 for all x.
How close must x0 be to τ for the method to converge?

Suppose we want to apply Newton’s method to solving f(x) = 0
where f is such that |f′′(x)| ? 10 and |f′(x)| ? 2 for all x. How
close must x0 be to τ for the method to converge?

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