Sam L.

asked • 04/30/20

Local extrema problem. PLEASE HELP!!

Find all local extrema of the function f(x)= 1/x-1 + 1/x on the interval (0,1).

Steven K.

Please check your problem to make sure it is correct: It should read f(x) = 1/(x-1) - 1/x
Report

04/30/20

Sam L.

no it is written the right way
Report

04/30/20

Paul M.

tutor
You mean it should be (2/x)-1? I, like Steven K., doubt it. In either case there are no local extrema.
Report

04/30/20

Doug C.

Sam, could it be that the text is using horizontal bar (vinculum) to separate the fractions into numerator and denominator? As in: 1 f(x) = ------- x - 1 If that is the case, when you end up using "/" to pose the problem you should group the terms in numerator and denominator to make the definition of the function clear.
Report

04/30/20

Doug C.

Well WyzAnt did not format my "as in" equation correctly. Hopefully you got the idea.
Report

04/30/20

Sam L.

It should be 1 over x-1 plus 1 over x. They are fractions
Report

04/30/20

1 Expert Answer

By:

Doug C. answered • 04/30/20

Tutor
5.0 (1,553)

Math Tutor with Reputation to make difficult concepts understandable

See tutors like this
See tutors like this

f(x) = (x-1)-1 + x-1


f'(x) = -1(x-1)-2 - x-2


f'(x) = -1/(x-1)2 - 1/x2


When does f'(x) = 0? Never. Do you see that? That means there are no horizontal tangent lines. so no local max or min. As a matter of fact f' is always negative so the function is always decreasing.There are vertical asymptotes as x=0 and x=1. Check it out on Desmos:


desmos.com/calculator/j0ocsgftpb


Upvote • 0 Downvote
More
Report

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.