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

    0
    ReputationRep:
    How do I solve: 4x^3-3x^4=0.5?
    Offline

    0
    ReputationRep:
    Perhaps using an iterative method like Newton Raphson,or you could rearrange it into f(x) = 0 and try and guess factors.
    Offline

    0
    ReputationRep:
    (Original post by fishpaste)
    Perhaps using an iterative method like Newton Raphson,or you could rearrange it into f(x) = 0 and try and guess factors.
    Hmm, since I still haven't studied the Newton-Raphson method I used another weird (and probably incorrect) method: logarithms.

    I ended up with x =~ 1.33, is that right?
    • Thread Starter
    Offline

    0
    ReputationRep:
    Well the actual question is from S3:

    The Continuous random variable Y has pdf f(y) defined by:
    f(y)=12y^2(1-y) for 0<y<1, 0 otherwise
    Find the median:
    so you want when p<y=0.5
    So i did this by integrating 12y^2-12y^3
    which is 4y^3-3y^4 = 0.5.
    (then someone's going to tell me i've integrated it wrong!)

    Due to the nature of question I would have thought there would be an exact answer using a method, other than Newton Raphson, etc etc...
    Offline

    11
    ReputationRep:
    Yeah, a numerical method would be best (Newton Raphson is fine). Sketch a graph and you'll see there are two solutions.

    I get 0.6143 and 1.2475 as my solutions to 4DP.
    Offline

    14
    ReputationRep:
    (Original post by sweetymango)
    How do I solve: 4x^3-3x^4=0.5?
    Draw the curve 4x^3 - 3x^4 = y and the line y = 0.5, where they cross should be the roots.

    There are no nice factors of 8x^3 - 6x^4 - 1 that I can see, so an approximations might be the best you can get from me...
    Offline

    0
    ReputationRep:
    haha I don't suppose this is the MEI S3 book?
    We just started that and it had a few questions like that and we were told not to bother doing them by our teacher because a) they are unsoluable using methods they expect for s3 and b) we'd never get asked such a thing in an exam. In fact our teacher said it probably was an error in printing.
    Offline

    11
    ReputationRep:
    That is a rather unusual answer for a stats question I must admit. They wouldn't expect you to know Newton-Raphson for an S3 paper.
    • Thread Starter
    Offline

    0
    ReputationRep:
    Yeah i understand your methods...i think the book must have done a printing error...or some sort...as it thinks the answer is 2/3
    Offline

    2
    ReputationRep:
    (Original post by sweetymango)
    Yeah i understand your methods...i think the book must have done a printing error...or some sort...as it thinks the answer is 2/3
    2/3 is the mode.
 
 
 
Poll
Do you agree with the proposed ban on plastic straws and cotton buds?
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.