Question

Use Newton’s method to approximate the root of x^2 + 4x + 2 = 0 between x = -4
and x = -3 .

Answer 1

Starting at -3:

h(-3.00000) = 23.00000 -- next x: -0.70000
h(-0.70000) = 5.29000 -- next x: 0.27963
h(0.27963) = 0.95967 -- next x: 0.55854
h(0.55854) = 0.07779 -- next x: 0.58553
h(0.58553) = 0.00073 -- next x: 0.58579
h(0.58579) = 0.00000 -- next x: 0.58579

Starting at -4:


h(-4.00000) = 34.00000 -- next x: -1.16667
h(-1.16667) = 8.02778 -- next x: 0.10088
h(0.10088) = 1.60667 -- next x: 0.52388
h(0.52388) = 0.17893 -- next x: 0.58449
h(0.58449) = 0.00367 -- next x: 0.58579
h(0.58579) = 0.00000 -- next x: 0.58579

Answer 2

My bad. Misplaced a + sign.


h(-4.00000) = 2.00000 -- next x: -3.50000
h(-3.50000) = 0.25000 -- next x: -3.41667
h(-3.41667) = 0.00694 -- next x: -3.41422
h(-3.41422) = 0.00001 -- next x: -3.41421