I had to miss the lesson for this in my math class cuz i had to take stupid standardized tests and i don't think i fully understand it... so i have to find two consecutive iterations that are withing .001 of eachother for the function f(x) = 3√(x-1) - x i got f'(x) = (3-2√(x-1))/(2√(x-1)) as the derivative i started with x1 = 1 and got these iterations x2 = 1.5 x3 = 1.189 x4 = 1.131 x5 = 1.153 x6 = 1.140 x7 = 1.149 and i began to get confused because my iterations kept going in that pattern bigger than smaller and i got really confused so if somebody could please explain to me what maybe i'm doing wrong, and also is there any way to find a better x1 that can put me closer without actually solving the equation for the zeros cuz i really don't feel like doing 10 iterations of every function i have to solve lol
The derivative is 3/(2sqrt(x-1)) - 1 The starting value shouldn't matter too much (as long as you're not 100 away or something) since Newton's method converges quadratically.
ok so if the function has multiple zeros would that mean i have to do that multiple times to find the different zeros and start with different starting values?