Numerical methods 23

Question 1

Find a root in the interval…

Answer 1

change of sign

Question 2

Change of sign summary sentence

Answer 2

since f(x) is continuous, there is a root in the interval…

Question 3

Failure of the change of sign method

Answer 3

odd numbers of roots
no change of sign but there are two roots
CoS but there is a vertical asymptote an f(x) is not continuous

Question 4

Staircase + cobweb

Answer 4

Vertical to the curve, horizontal to the line

Question 5

Failure of iterative methods

Answer 5

will only find a root in -1<g’(a)<1

Question 6

Failure of newton raphson

Answer 6

if starting point is close to stationary point, may converge at the wrong root
will fail if grad is 0