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

    14
    ReputationRep:
    The question is:  f(x) = x/x^2+2 Find the set of values of x for which f'(x)<0
    • TSR Support Team
    • Clearing and Applications Advisor
    Online

    21
    ReputationRep:
    (Original post by AxSirlotl)
    The question is:  f(x) = x/x^2+2 Find the set of values of x for which f'(x)<0
    The first step is obviously to get an expression for f'(x), have you managed to do that?
    • Thread Starter
    Offline

    14
    ReputationRep:
    (Original post by Plagioclase)
    The first step is obviously to get an expression for f'(x), have you managed to do that?
    yeah boii
    • Official TSR Representative
    Offline

    11
    ReputationRep:
    (Original post by AxSirlotl)
    The question is:  f(x) = x/x^2+2 Find the set of values of x for which f'(x)<0
    You have to use the quotient rule and then look at the numerator.

    Could you show your workings?
    • TSR Support Team
    • Clearing and Applications Advisor
    Online

    21
    ReputationRep:
    (Original post by AxSirlotl)
    yeah boii
    Well then, you've got your inequality, you just need to solve that.
    • Thread Starter
    Offline

    14
    ReputationRep:
    (Original post by BrasenoseAdm)
    You have to use the quotient rule and then look at the numerator.

    Could you show your workings?
    I got  f'(x) = -2x^2/x^2+2
    Sorry, I can't do proper fractions because I don't understand the guide heh
    • Community Assistant
    Offline

    18
    ReputationRep:
    (Original post by AxSirlotl)
    I got  f'(x) = -2x^2/x^2+2
    Sorry, I can't do proper fractions because I don't understand the guide heh
    Your derivative is wrong. To write a fraction it's \frac{numerator}{denominator}, but the notation you're using is acceptable anyway.
    • Official TSR Representative
    Offline

    11
    ReputationRep:
    (Original post by NotNotBatman)
    Your derivative is wrong. To write a fraction it's \frac{numerator}{denominator}, but the notation you're using is acceptable anyway.
    Does TSR detect LaTex automatically? We tried replying with the coding:

    \frac{x}{x^2+2}

    &

    [tex]\frac{x}{x^2+2}
    • Community Assistant
    Offline

    18
    ReputationRep:
    (Original post by BrasenoseAdm)
    Does TSR detect LaTex automatically? We tried replying with the coding:

    \frac{x}{x^2+2}

    &

    [tex]\frac{x}{x^2+2}
    [tex] maths things go here [/ tex] , but without the space after the /
    • Thread Starter
    Offline

    14
    ReputationRep:
    (Original post by NotNotBatman)
    Your derivative is wrong. To write a fraction it's \frac{numerator}{denominator}, but the notation you're using is acceptable anyway.
    I keep getting the same answer ;-;

    I tried doing fractions but it kept putting my numerator in front of my fraction and leaving the top of the fraction blank, so I can't really show my working very easily.
    • Official TSR Representative
    Offline

    11
    ReputationRep:
    (Original post by AxSirlotl)
    I keep getting the same answer ;-;

    I tried doing fractions but it kept putting my numerator in front of my fraction and leaving the top of the fraction blank, so I can't really show my working very easily.
    Thanks for the LaTex tip!

    Problem: differentiate \frac{x}{x^2+2}

    Technique: quotient rule \frac{vu' - uv'}{v^2}

    u = x and v = X^2+2, u' = derivative of u and v'= derivative of v
    Online

    10
    ReputationRep:
    Use the chain rule for differentiation:

    h(x) = f(x)/g(x)

    h'(x) = f'(x)g(x)-f(x)g'(x) / [g(x)]^2

    The last step is trivial; let the inequality be less than 0 and solve it accordingly.
    Offline

    16
    ReputationRep:
    Is that  \frac{x}{x^2} + 2 or  \frac{x}{x^2+2}
    • Thread Starter
    Offline

    14
    ReputationRep:
    (Original post by zeldor711)
    Is that  \frac{x}{x^2} + 2 or  \frac{x}{x^2+2}
    The latter
    • Thread Starter
    Offline

    14
    ReputationRep:
    (Original post by BrasenoseAdm)
    Thanks for the LaTex tip!

    Problem: differentiate \frac{x}{x^2+2}

    Technique: quotient rule \frac{vu' - uv'}{v^2}

    u = x and v = X^2+2, u' = derivative of u and v'= derivative of v
    (Original post by thekidwhogames)
    Use the chain rule for differentiation:

    h(x) = f(x)/g(x)

    h'(x) = f'(x)g(x)-f(x)g'(x) / [g(x)]^2

    The last step is trivial; let the inequality be less than 0 and solve it accordingly.
    I got my derivative as -1/(x^2+2), is that right ;-;
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    (Original post by AxSirlotl)
    I got my derivative as -1/(x^2+2), is that right ;-;
    Not quite.

    If you post your working we would just be able to spot where you're going wrong.
    • Thread Starter
    Offline

    14
    ReputationRep:
    (Original post by RDKGames)
    Not quite.

    If you post your working we would just be able to spot where you're going wrong.
    Using the quotient rule:

    u = x v = x^2 + 2

    u' = 1 v' = 2x

    Then I got
    numerator: (x^2 + 2) - 2x^2

    denominator: (x^2 + 2)^2

    So on the top I had v x u' - u x v' all over v^2
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    (Original post by AxSirlotl)
    Using the quotient rule:

    u = x v = x^2 + 2

    u' = 1 v' = 2x

    Then I got
    numerator: (x^2 + 2) - 2x^2

    denominator: (x^2 + 2)^2

    So on the top I had v x u' - u x v' all over v^2
    OK, so how did you go from \frac{2-x^2}{(x^2+2)^2} to -\frac{1}{x^2+2}?
    • Thread Starter
    Offline

    14
    ReputationRep:
    (Original post by RDKGames)
    OK, so how did you go from \frac{2-x^2}{(x^2+2)^2} to -\frac{1}{x^2+2}?
    I've just realised that's wrong, I mean I've had another go at it and I'm back to (-x^2 + 2)/(x^2+2)^2
    I'm not sure where to go from there, if I need make that into an inequality then I'm not sure what to do after that.
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    (Original post by AxSirlotl)
    I've just realised that's wrong, I mean I've had another go at it and I'm back to (-x^2 + 2)/(x^2+2)^2
    I'm not sure where to go from there, if I need make that into an inequality then I'm not sure what to do after that.
    (x^2+2)^2 &gt; 0 so \frac{2-x^2}{(x^2+2)^2} &lt;0 \Rightarrow 2-x^2 &lt;0
 
 
 
  • 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
    Did TEF Bronze Award affect your UCAS choices?
    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.