Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    19
    http://mathsathawthorn.pbworks.com/f/FP1Jan07.pdf
    In q6a we have to find the coordinates of the stationary point on the graph of f so so far ive worked out dy/dx which is (-2ylnx)/x and i know at a stationary point dy/dx=0 , but what do i do next?
    • Study Helper
    Online

    13
    Study Helper
    (Original post by Ayaz789)
    http://mathsathawthorn.pbworks.com/f/FP1Jan07.pdf
    In q6a we have to find the coordinates of the stationary point on the graph of f so so far ive worked out dy/dx which is (-2ylnx)/x and i know at a stationary point dy/dx=0 , but what do i do next?
    Substitute in the value of y, and look for where the numerator is zero, i.e. one of the multiplicands is zero. Note that the domain is restricted to x > 0.
    • Thread Starter
    Offline

    19
    (Original post by ghostwalker)
    Substitute in the value of y, and look for where the numerator is zero, i.e. one of the multiplicands is zero. Note that the domain is restricted to x > 0.
    So if -2ylnx=0 How do i know the value of y and x?
    • Study Helper
    Online

    13
    Study Helper
    (Original post by Ayaz789)
    So if -2ylnx=0 How do i know the value of y and x?
    You're told y as a function of x at the start, so sub that in, and you now have a product of functions of x. For that to equal zero, one of the multiplicands must be zero. Check each one to find what value of x - if any - will make it zero.
    • Thread Starter
    Offline

    19
    (Original post by ghostwalker)
    You're told y as a function of x at the start, so sub that in, and you now have a product of functions of x. For that to equal zero, one of the multiplicands must be zero. Check each one to find what value of x - if any - will make it zero.
    Step at a time please Okay so i have put they y value into x to get 0=-2^-lnx.lnx as the x cancels out?
    • Study Helper
    Online

    13
    Study Helper
    (Original post by Ayaz789)
    Step at a time please Okay so i have put they y value into x to get 0=-2^-lnx.lnx as the x cancels out?
    EEK!!!! The x does not cancel.

    dy/dx = -2x^{-ln x}{ln x}/x

    = -2x^{-(ln x)-1}{ln x} = 0

    So, either

    ln x = 0, or

    -2x^{-(ln x)-1} = 0

    and recall that x>0, so can that second part ever be zero?
    • Thread Starter
    Offline

    19
    (Original post by ghostwalker)
    EEK!!!! The x does not cancel.

    dy/dx = -2x^{-ln x}{ln x}/x

    = -2x^{-(ln x)-1}{ln x} = 0

    So, either

    ln x = 0, or

    -2x^{-(ln x)-1} = 0

    and recall that x>0, so can that second part ever be zero?
    -2x^{-(ln x)-1}{ln x} = 0 where did the -1 come from? Im really sorry but idk :/
    • Study Helper
    Online

    13
    Study Helper
    (Original post by Ayaz789)
    -2x^{-(ln x)-1}{ln x} = 0 where did the -1 come from? Im really sorry but idk :/
    Rules of indices.

    In essence,

    x^a/ x = x^a / x^1 = x^(a-1)
    • Thread Starter
    Offline

    19
    (Original post by ghostwalker)
    Rules of indices.

    In essence,

    x^a/ x = x^a / x^1 = x^(a-1)
    Ohh yhhhh
    • Thread Starter
    Offline

    19
    (Original post by ghostwalker)
    EEK!!!! The x does not cancel.

    dy/dx = -2x^{-ln x}{ln x}/x

    = -2x^{-(ln x)-1}{ln x} = 0

    So, either

    ln x = 0, or

    -2x^{-(ln x)-1} = 0

    and recall that x>0, so can that second part ever be zero?
    Thank you!
    • Thread Starter
    Offline

    19
    (Original post by ghostwalker)
    Rules of indices.

    In essence,

    x^a/ x = x^a / x^1 = x^(a-1)
    I need help!
    • Study Helper
    Online

    13
    Study Helper
    (Original post by Ayaz789)
    I need help!
    Focus - be specific.

    Or is that just a general exclamation, for which you're not expecting a reply?
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    What's your favourite Christmas sweets?
    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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