Require two initial guesses to begin the algorithm

Use a gradient to approximate the next guess of the root

Are sensitive to the shape of the function

May diverge when approximating the next guess of the root

6.2470

3.247

–3.2470

–0.24704

Exact derivative of the function is required

Mid-point is calculated to determine the root estimate

One initial guess with a perturbation is required to begin the algorithm

Derivative is approximated using a chord

-1.8988,2.9891 & 12.6711.

-1.8654, 2.6982 & 10.8924. 

There are only two roots which are -1.1454 and 2.4910

There is only one root which is -1.7689

-2.1221, 2.7797 & 9.8804.

-1.6331, 3.5657 & 11.1678.

-1.7689, 2.5178 & 11.5642.

-1.1454, 2.4910 & 9.0988.

only the secant method.

only the Newton-Raphson method.

only the bisection and false position methods.

only the Newton-Raphson, secant and modified secant methods. 

only the bisection, false position and Newton-Raphson methods.

all of the methods: bisection, false position, Newton-Raphson, secant and modified secant.

none of the methods as the function never touches the x axis.

the false position method but not the bisection method.

False position

Bisection

Newton-Raphson

All of the above

a and b are of the same sign

Function values at a and b are of the same sign

Function values at a and b are of opposite signs

a and b are of opposite signs

If f(x_r)*f(x_u) < 0, then x_u = (x_r + x_l)/2 and x_l = (x_r + x_u)/2.

If f(x_l)*f(x_r) < 0, then x_l = x_r and x_u stays the same.

If f(x_r)*f(x_u) < 0, then x_u = x_r and x_l stays the same.

If f(x_r)*f(x_u) > 0, then x_l = x_r and x_u stays the same.

If f(x_l)*f(x_r) > 0, then x_u = x_r and x_l stays the same.

If f(x_r)*f(x_u) > 0, then x_u = (x_r + x_l)/2 and x_l = (x_r + x_u)/2.

If f(x_r)*f(x_u) > 0, then x_u = x_r and x_l stays the same. 

If f(x_r)*f(x_u) > 0, then x_u = (x_r + x_u)/2 and x_l = (x_r + x_l)/2.