Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    Could anyone please show me how to work this out as I cannot get the correct answer?

    If f(x) = x sin^2 x, find f ' (pie/6).

    Thanks
    Offline

    0
    ReputationRep:
    What did you get for f'(x)?
    • Thread Starter
    Offline

    0
    ReputationRep:
    f ' (x) = x(2sinxcosx) + sin^2 x

    2sinxcosx = sin2x

    f ' (x) = xsin2x + sin^2 x
    Offline

    0
    ReputationRep:
    That's correct. What did you get when you set x=\frac{\pi}{6}?
    Offline

    13
    ReputationRep:
    now just substitute x = pi/6
    • Thread Starter
    Offline

    0
    ReputationRep:
    The book says that the answer is 1/4 ( 1+pie/root3 )

    But the closest that I can get is pie/6 (2root3/4) + 1/4

    I know where the 1 comes from, but its the pie/root3 that I cannot get.
    Offline

    16
    ReputationRep:
    f(x)= sin^2x = (sinx)^2

    f'(x)= 2sinx . cosx = 2sinxcosx (using the chain rule)

    now just sub pie/6 into x

    pretty sure that is right however haven't done maths since my last exam in june
    (btw radians)
    Offline

    0
    ReputationRep:
    (Original post by katbro20)
    The book says that the answer is 1/4 ( 1+pie/root3 )

    But the closest that I can get is pie/6 (2root3/4) + 1/4
    Aren't these equivalent? Try rationalising the denominator of the book's answer and see if you can show they're the same.
    Offline

    16
    ReputationRep:
    soory, didn't see the x at the beginning
    Offline

    16
    ReputationRep:
    f(x)=xsin^2x u= x u'=1 v=sin^2x = (sinx)^2 v'= 2sinxcosx

    f'(x)= x(2sinxcosx) + sin^2x

    2sinxcosx = sin2x (double angle)

    therefore, f'(x) = xsin2x + sin^2x (now just sub pie/6 in to x)
    Offline

    16
    ReputationRep:
    the answer is 0.7034
    • Thread Starter
    Offline

    0
    ReputationRep:
    Thats where I got up to.

    The problem that I am having is substituting in the pie/6
    Offline

    16
    ReputationRep:
    do it one at a time, don't enter it all into the calculator at once e.g. find sin2(pie/6), then multiply that answer by pie/6 etc
    • Thread Starter
    Offline

    0
    ReputationRep:
    no calculator. The answer is given as 1/4 (1 + pie/root3)
    Offline

    16
    ReputationRep:
    (Original post by katbro20)
    Thats where I got up to.

    The problem that I am having is substituting in the pie/6
    is your calculator on radians mode? (Most common mistake)
    Offline

    0
    ReputationRep:
    Am I missing something obvious?
    Hasn't she got the right answer already? :confused:
    Offline

    16
    ReputationRep:
    don't know how they got that but its equivalent to the decimal value (0.7034), so they won't mark you down if like you done that in the exams
    Offline

    0
    ReputationRep:
    Yeah, their answer is an a slightly unusual form. Not too hard to show they're equivalent though.
    • Thread Starter
    Offline

    0
    ReputationRep:
    OK. Lets see if I can do this.

    If pie/6 (2root3/4) + 1/4 = 1/4 (1 + pie/root3)

    Then pieroot3/12 + 1/4 must = 1/4 + pie/4root3

    pieroot3/12 = pie/4root3

    pieroot3/3 = pie/root3 reverse of rationalising

    which gives pie/root3 = pie/root3

    Unless my logic has gone wrong somewhere, they are equal (thanks Calira), therefore, I must be able to change my version into their version some how.
    • Thread Starter
    Offline

    0
    ReputationRep:
    Thanks everyone. Finally managed to do it.

    Now it is do, I cannot believe that I missed taking out the common factor from the first part of the function.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: August 30, 2008

University open days

  • University of Lincoln
    Mini Open Day at the Brayford Campus Undergraduate
    Wed, 19 Dec '18
  • University of East Anglia
    UEA Mini Open Day Undergraduate
    Fri, 4 Jan '19
  • Bournemouth University
    Undergraduate Mini Open Day Undergraduate
    Wed, 9 Jan '19
Poll
Were you ever put in isolation at school?
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

Equations

Best calculators for A level Maths

Tips on which model to get

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.