Question

please help!!!!Apply newtons method to approximate the x-values of the indicated points of intersection of the 2 graphs. continue the process until 2 successive approximations differ by less than 0.001. (Hint: Let h(x)=f(x)-g(x))
f(x)=x^6
g(x)=cos(x)
x= ??? (smaller value)
x=??? (larger value)

Thanks!!

Answer 1

As often is the case, the starting point can make a difference. I started at x=1.1


h(1.10000) = 1.31796 -- next x: 0.97512
h(0.97512) = 0.29866 -- next x: 0.92631
h(0.92631) = 0.03093 -- next x: 0.91998
h(0.91998) = 0.00045 -- next x: 0.91989

Answer 2

Starting at x=0.1, things take a bit longer to converge:


h(0.10000) = -0.99500 -- next x: 10.06065
h(10.06065) = 1036945.84148 -- next x: 8.38387
h(8.38387) = 347270.57671 -- next x: 6.98656
h(6.98656) = 116299.56298 -- next x: 5.82215
h(5.82215) = 38948.45732 -- next x: 4.85180
h(4.85180) = 13044.10696 -- next x: 4.04313
h(4.04313) = 4368.84599 -- next x: 3.36910
h(3.36910) = 1463.42243 -- next x: 2.80716
h(2.80716) = 490.27325 -- next x: 2.33854
h(2.33854) = 164.25215 -- next x: 1.94780
h(1.94780) = 54.97734 -- next x: 1.62277
h(1.62277) = 18.31398 -- next x: 1.35550
h(1.35550) = 5.98917 -- next x: 1.14486
h(1.14486) = 1.83849 -- next x: 1.00022
h(1.00022) = 0.46121 -- next x: 0.93287
h(0.93287) = 0.06355 -- next x: 0.92027
h(0.92027) = 0.00182 -- next x: 0.91989
h(0.91989) = 0.00000 -- next x: 0.91989