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

    15
    ReputationRep:


    I managed to do part a) without much issue, but part b) I did with by substitution, which was not the method on the mark scheme and apparently, not the right answer. Where did I make the mistake in my workings?

    Offline

    2
    ReputationRep:
    I think you put x=3 into f(x) so f(3)=....

    Don't no exactly until I do the whole question. If that not right let me no I will do the question for you
    Offline

    22
    ReputationRep:
    (Original post by frostyy)
    ...
    You were doing perfectly fine right up till \displaystyle t + \frac{9}{t} = 10.

    To get this into a quadratic, you need to multiply both sides by t which gets you t^2 + 9 = 10t \Rightarrow t^2 - 10t + 9 = 0 which gives you your values of t. I'm not sure what you seem to have done.
    Offline

    22
    ReputationRep:
    (Original post by Aaliyah.97)
    I think you put x=3 into f(x) so f(3)=....

    Don't no exactly until I do the whole question. If that not right let me no I will do the question for you
    It's not right. You don't know what f(x) is. Also don't bother doing the question for him, full solutions are against forum guidelines.
    Offline

    2
    ReputationRep:
    (Original post by Zacken)
    It's not right. You don't know what f(x) is. Also don't bother doing the question for him, full solutions are against forum guidelines.
    Ooh okay I didn't know that I'm knew here so sorry
    Offline

    1
    ReputationRep:
    Don't you just do the original equation they gave you (as it is the differentiated equation) equal to 10 and the two values of x you find is your answer
    Offline

    22
    ReputationRep:
    (Original post by Aaliyah.97)
    Ooh okay I didn't know that I'm knew here so sorry
    No problem! :-)
    Offline

    22
    ReputationRep:
    (Original post by Student232)
    Don't you just do the original equation they gave you (as it is the differentiated equation) equal to 10 and the two values of x you find is your answer
    Yes. That's precisely what he's done, except for a small slip when trying to solve his quadratic in \sqrt{x}.
    • Thread Starter
    Offline

    15
    ReputationRep:
    (Original post by Zacken)
    You were doing perfectly fine right up till \displaystyle t + \frac{9}{t} = 10.

    To get this into a quadratic, you need to multiply both sides by t which gets you t^2 + 9 = 10t \Rightarrow t^2 - 10t + 9 = 0 which gives you your values of t. I'm not sure what you seem to have done.
    Thanks so much! I tried to get rid of the (9/t) by multiplying both sides by 9. Not sure why I thought of that, but it didn't occur to me that that was were the issue was lying. Anyway, thanks a lot
    Offline

    22
    ReputationRep:
    (Original post by frostyy)
    Thanks so much! I tried to get rid of the (9/t) by multiplying both sides by 9. Not sure why I thought of that, but it didn't occur to me that that was were the issue was lying. Anyway, thanks a lot
    No problem!

    You might have been able to avoid this issue by having done f'(x) = 10 straight away; that is:

    \displaystyle

\begin{equation*}\frac{x+ 9}{\sqrt{x}} = 10 \iff x+9 = 10\sqrt{x} \iff x - 10\sqrt{x} + 9 = 0\end{equation*}

    Then the substitution t = \sqrt{x} gives you

    \displaystyle

\begin{equation*}t^2 - 10t +9  = 0\end{equation*}

    But your method was essentially the same and just as nice, really!
    Offline

    1
    ReputationRep:
    (Original post by Zacken)
    Yes. That's precisely what he's done, except for a small slip when trying to solve his quadratic in \sqrt{x}.
    Sorry I didn't look at the working haha only the question
    Offline

    22
    ReputationRep:
    (Original post by Student232)
    Sorry I didn't look at the working haha only the question
    Yeah, don't worry, I'm guilty of doing that far too often. :lol:
 
 
 
  • 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
    Brussels sprouts
    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.