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

Differentiation Question. HELP NEEDED URGENTLY! watch

    • Thread Starter
    Offline

    0
    ReputationRep:
    This is really frustrating me!!

    Q: Two real numbers x and y are such that 2x+y=100.
    find the maximum value of the product of the two numbers.


    Please please please help me!
    Offline

    0
    ReputationRep:
    y=100-2x
    x=(100-y)/2

    x*y=?

    Rerrange to get only x on RHS...
    • Thread Starter
    Offline

    0
    ReputationRep:
    I'm sorry but I can't see how this helps?
    Offline

    0
    ReputationRep:
    answer is 1250
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by crimsonmist2)
    answer is 1250
    How did you work that out? :confused: it would be very helpful if you could share your wisdom. thanks.
    Offline

    0
    ReputationRep:
    2x+y=100
    if you multiply the whole thing by x,
    2x^2 + yx = 100x
    so
    yx= 100x - 2x^2
    therefore yx is a function of x
    so if you differentiate yx with resp to x
    its equal to: 100-4x
    so to find maxima put that = 0 and solve
    you get x= 25
    to find the value of xy, you put x= 25 into 100x- 2x^2
    and you get 1250
    Offline

    0
    ReputationRep:
    ok?
    • Thread Starter
    Offline

    0
    ReputationRep:
    Thank you very much, makes perfect sense!
    Offline

    0
    ReputationRep:
    If you had read my post and actually thought about what i said instead of expecting someone to give you the answer you'd have realised it was actually a rather helpful reply.
    • Thread Starter
    Offline

    0
    ReputationRep:
    the whole reason i put this post up was to get help with doing the question. i didnt just ask for the answer.
    if you just told me what to do without doing it, that would have been great.
    giving just the answer was no help at all!
    Offline

    3
    ReputationRep:
    x.y = x(100-2x)
    = -2x^2 + 100x
    = -2(x-25)^2 +1250
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: February 6, 2010
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.