Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    I'm trying to show the minimum value of y = x² -lnx is 1/2(1+ln2)

    I think you have to differentiate so I get 2x - 1/x

    To find stationary points dy/dx = 0 so 2x - 1/x = 0

    A bit of fiddling gives x = ±root1/2

    Assuming this bit is right, where do I go from here? I'm guessing I should differentiate again and find the maximum/minimum points, but doing so wont have anything to do with ln2 in it...

    Any ideas TSR?
    Offline

    14
    No, imtired. We know that log(x) is only real for x>0, so we don't need to differentiate again.

    OP: Substitute your value of x back in to find y. A little bit of fiddling gives the ln(2).
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Kolya)
    No, imtired. We know that log(x) is only real for x>0, so we don't need to differentiate again.

    OP: Substitute your value of x back in to find y. A little bit of fiddling gives the ln(2).
    Plugging in root1/2 gives y = 1/2 - ln(root1/2) (the other value of x is not needed because you cant get the ln of a minus number)

    So y = 1/2 - ln1 - ln(root2)

    This gives 1/2 + ln(root2) and not ln2...
    where am I going wrong?
    Offline

    8
    ReputationRep:
    (Original post by ChrisKing)
    Plugging in root1/2 gives y = 1/2 - ln(root1/2) (the other value of x is not needed because you cant get the ln of a minus number)

    So y = 1/2 - ln1 - ln(root2)

    This gives 1/2 + ln(root2) and not ln2...
    where am I going wrong?
    \ln \sqrt2 = \ln 2^{\frac{1}{2}}

    Laws of logs anyone?
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by sonofdot)
    \ln \sqrt2 = \ln 2^{\frac{1}{2}}

    Laws of logs anyone?
    Oh dear, I love the way I forget my core 1 and 2 stuff

    Thank you!
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: November 8, 2008
Poll
Do I go to The Streets tomorrow night?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.