This question concerns Newton's method. It can find a precise solution of an equation, but often needs a good starting-point. The following function has three zeros.
a) Let f(x)=(23/100)x+cosx.Apply Newton's method to f(x)starting with x0=-1. Enter (x1,x2,x3),rounded to four places after the decimal?
b) Sometimes, if the initial point is not near a solution, Newton's method is not effective. Repeat the previous question, but this time with x0=0.(Also consider graphically what is happening.)?
c) The function has two other real roots, between 0 and 10. Find initial values x0for which Newton's method approaches each of the other two roots. Give the other two roots to four decimal places (again using round brackets)?