Numerical Methods

Question 1

How to find roots of f(x)

Answer 1

Sign changes in small interval of x, only if function is continuous

Question 2

When can sign change method fail?

Answer 2

Many roots in interval

If function not continuous, the sign change could mean there is an asymptote

Question 3

Iteration method

Answer 3

Rearrange f(x), so atleast 1 x = f(x)
Interactive formula: x n+1 = f(xn)
When x no longer changes, that is the root

Also, draw cobweb diagrams and staircase diagrams converging

Question 4

Newton-Raphson method

Answer 4

X n+1 = x n - (f(xn)/f’(xn))

Question 5

When does newton-raphson method fail?

Answer 5

Stationary point, since derivative will be 0 and you cannot divide by 0
When gradient is really small