Hey there! Sign in to join this conversationNew here? Join for free

Natural logarithmic equation help s'il vous plait Watch

    • Official TSR Representative
    Offline

    11
    ReputationRep:
    (Original post by jessyjellytot14)
    "Prove, by counter-example, that the statement
    “ln (3x 2 + 5x + 3) ≥ 0 for all real values of x” is false."

    Hmmm I'm not quite sure how to go about this so i'll post my working below & could you check it please?

    Also can some explain what a real number is? I don't do further maths but I'm assuming it's just a whole integer.. So for example, -2/3 isn't a real number...?

    Thanks

    Another way of doing this is to differentiate the expression and set the first derivative to equal zero in order to find the value of x that minimises y. You can then see if this makes f(x) => 0.

    Let y = ln(u) where u = (3x^2 + 5x + 3). du/dx = 6x + 5, dy/du = 1/(3x^2 + 5x + 3).
    so dy/dx = (6x + 5) / (3x^2 + 5x + 3). dy/dx = 0 when 6x + 5 = 0, so 6x = -5, and x = -5/6.

    Sub in x = - 5/6 and you have your proof by counter-example.
 
 
 
  • 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
    Will you be richer or poorer than your parents?
    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.