11. min and max/ NR

Question 1

What is the newton ramphson method?

Answer 1

When tangents at x1 that cross x axis are found to approximate roots of x1

Question 2

When and why is the NR method not suitable?

Answer 2

• At a turning point the tangent will be horizontal which would cause a division of zero
• If it is close to a turning point it will converge slowly

Question 3

What is the formula?

Answer 3

x1 subtract f(x1) / f’(x1)

Question 4

What is something that can happen when applied to modelling?

Answer 4

-When being used on a max or min, use the f’(x) as first function.

Question 5

how to show that a coordinate is correct to certain amount of dp?

Answer 5

• work out what it could have been rounded from upper and lower bound.
• Then sub in to show change of sign of continuous function

Question 6

How do you show cobwebs or staircases?

Answer 6

-Curve xn then line

Question 7

How do you prove that the newton raphson method can be written in a particular way?

Answer 7

-Create the formula using the expression and replace x for xn

Question 8

If a root is between 0 and 1 how can you find the root using newton raphson method?

Answer 8

-Keep subbing in 0.5 into the newton raphson method until It converges.

Question 9

How do you explain that the newton raphson method cannot be used for a good approximation?

Answer 9

-Draw in the first vertical line then draw in the tangent, then where this cuts the x axis is no longer in the interval.