Question

Find the x-coordinate of local maximum and local minimum of the function f(x)=x^5-x^4+x^2-x on interval negative infinity to infinity. to 6 decimal accuaracy.

Is this just newtons theory or what else do i do?

Answer 1

differentiate f(x) and find the turning points....

Answer 2

i use the newtons method on f'(x) to find the points?

Answer 3

Find the critical points

Answer 4

i use the newtons method on f'(x) to find the points?

yep.

Answer 5

I don't know the newton's method O.O I just do as irishboy said and take the derivative to find the critical points

Answer 6

okay lol since the derivative is to the x^5 ill use newtons method1

Answer 7

can you link to that? I've never heard of it

Answer 8

http://tutorial.math.lamar.edu/Classes/CalcI/NewtonsMethod.aspx

Answer 9

Here are the steps i took. i took the derivative of f(x).
then to find the critical points of the derivative to see where it increases and decreases. i took the derivative of the derivative so i could use newtons method. then using newtons method i got that the critical points were
rel min occurs when x=.607880
rel max occurs when x=-.688350

does it sound right?

Answer 10

anyone?

Answer 11

https://www.wolframalpha.com/input/?i=plot+x%5E5-x%5E4%2Bx%5E2-x+from+-.75+to+.75

@eggshell
is this your curve? if so you can get a check yourself....

Answer 12

https://www.wolframalpha.com/input/?i=plot+5x%5E4-4x%5E3%2B2x-1+from+-1+to+1

better - the derivative...

Answer 13

ah ok, thanks, yea I've gone through the paces, but we never did that . Hmm Who knew?

Answer 14

Also, I still feel that just taking the derivative and setting =0 would be easier. You would have a maximum of 4 roots

Answer 15

@eggshell
i ran a little iteration in Excel and the roots are:

-0.68341137 & 0.60787236

your stuff looks pretty good to me.

Answer 16

Alright i hope im right lol

Answer 17

Refer to the attachment from the Mathematica 9 program.