Question

i have no idea how to approach this Newton's method problem! :( Please help!
Use Newton's method to approximate the given number correct to eight decimal places.
sixthroot(49)

Answer 1

\[\large \sqrt[6]{49}\]
\[\large x = 49^{\frac{1}{6} }\]
\[x ^{6} - 49 =0 \]
\[f(x) = x ^{6} - 49\] ;\(f'(x) = 6x ^{5}\)

Then use newton's method..

Answer 2

great! thanks! :) i'll try it out!

Answer 3

Also for picking initial guess:
you know its between 1 and 2 so use either 1 or 2 as initial guess

Answer 4

so i finished with 1.921875 after I used the initial guess as 2 and it was still wrong :/

Answer 5

try to keep going, sometimes you have to keep repeating the process to get more accurate answer

you can verify answer by calculating 6th root on your calculator

Answer 6

so kept going and ended with 1.91303459 and it was wrong :( i'm losing hope :/

Answer 7

haha you are getting closer

hint, unless you have to do it by hand i reccomend using a spreadsheet, then you can repeat it a bunch of times in a matter of seconds

Answer 8

oh wow thank you soooooo much!! TT v TT

Answer 9

welcome