Question

Mark T (true) or F (false). Justify your answer when it is false.

(a) The secant method is always guaranteed to converge, while Newton’s method is not.

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

(c) Newton’s method exhibits slower convergence than the secant method.

(d) We can use the bisection method to a function f(x) without having any knowledge of the derivative f′(x)

(e) In order to use the bisection method, we need to have a continuous function f(x), with continuous derivative f′(x).

(f) We cannot use Newton’s method to solve f(x) = 0 if the derivative f′(x) happens to be zero at the exact location of the solution.

Answer #1

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.

Consider the function f(x) = 1 2 |x|.
a) Can we use bisection search to find one of its roots? Why or
why not?
b) Can we use Newton’s method to find one of its roots? Why or
why not?

True or false justify your answer
1-The higher the price of X1 the flatter the B.L would be
2-Consumer equilibrium requires that indifference curve intersects
the B.L
3-If B.L slope =zero, then a consumer can have an extra unit of
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4-Cash subsidy is preferred to gift certificate from the store
owner view point

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y
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