Turn on thread page Beta
    • Thread Starter
    Offline

    12
    ReputationRep:
    The function f is defined for x ≥ 0. It is given that f has a minimum value when x = 2 and that f ′′(x) = (4x + 1)^-1/2.
    (i) Find f ′(x).
    It is now given that f ′′(0), f'(0) and f(0) are the first three terms respectively of an arithmetic progression.
    (ii) Find the value of f(0).
    (iii) Find f(x), and hence find the minimum value of f.
    Sol. (i) I got f'(x) by intergrating and finding the value of c and then substiuting the value of c to form the equation.
    y= (4x+1)^1/2-3)/2
    I am really confused on the second and third part. Please help.
    Offline

    13
    ReputationRep:
    Arithmetic progression means that they are in the form kth term = a + (k-1)d where a Is the first time and d is a common difference
    Posted on the TSR App. Download from Apple or Google Play
    Offline

    13
    ReputationRep:
    So find f’’(0) and f’(0). for f(0) you continue the pattern like an arithmetic progression. Then you can integrate f’(0) given that you now have the constant
    Posted on the TSR App. Download from Apple or Google Play
    • Study Helper
    Offline

    15
    Study Helper
    (Original post by kundanad)
    The function f is defined for x ≥ 0. It is given that f has a minimum value when x = 2 and that f ′′(x) = (4x + 1)^-1/2.
    (i) Find f ′(x).
    It is now given that f ′′(0), f'(0) and f(0) are the first three terms respectively of an arithmetic progression.
    (ii) Find the value of f(0).
    (iii) Find f(x), and hence find the minimum value of f.
    Sol. (i) I got f'(x) by intergrating and finding the value of c and then substiuting the value of c to form the equation.
    y= (4x+1)^1/2-3)/2
    I am really confused on the second and third part. Please help.
    (ii)

    For any AP, we have

    a0 = a
    a1 = a+d
    a2 = a+2d

    So, to start, can you work out a simple relationship between a0,a1,a2, eliminating a and d.

    Once you've got that equation, f'(0) and f''(0) are striaght forward, f(0) is unknown, and those are the three values to go into your relationship equation to find f(0).
    • Thread Starter
    Offline

    12
    ReputationRep:
    (Original post by ghostwalker)
    (ii)

    For any AP, we have

    a0 = a
    a1 = a+d
    a2 = a+2d

    So, to start, can you work out a simple relationship between a0,a1,a2, eliminating a and d.

    Once you've got that eqiatopm, f'(0) and f''(0) are striaght forward, f(0) is unknown, and those are the three values to go into your AP to find f(0).
    I am still confused. Can you make it more clear. Thank you.
    • Study Helper
    Offline

    15
    Study Helper
    (Original post by kundanad)
    I am still confused. Can you make it more clear. Thank you.
    Which bit?
    • Thread Starter
    Offline

    12
    ReputationRep:
    (Original post by ghostwalker)
    Which bit?
    From second part.
    • Study Helper
    Offline

    15
    Study Helper
    (Original post by kundanad)
    From second part.
    Of what? My answer, or the original question? Please be clear, and say what bit you'd don't understand, otherwise this is going to take hours.
    • Thread Starter
    Offline

    12
    ReputationRep:
    (Original post by ghostwalker)
    Of what? My answer, or the original question? Please be clear, and say what bit you'd don't understand, otherwise this is going to take hours.
    The original question with your answer as well. Thank you.
    • Study Helper
    Offline

    15
    Study Helper
    (Original post by kundanad)
    The original question with your answer as well. Thank you.
    The three terms, f ′′(0), f'(0) and f(0) are the first 3 terms of an AP.

    You can work out the first two, simply by substituting x=0, into the appropriate formula. f''(x), or f'(x).

    To find the third, f(0), we need to establish a relationship between all three, so we can form an equation, with the unknown f(0), and the two other known values.

    These three terms are the a0, a1, a2 of the AP.

    And follow my first post.
    • Thread Starter
    Offline

    12
    ReputationRep:
    (Original post by ghostwalker)
    The three terms, f ′′(0), f'(0) and f(0) are the first 3 terms of an AP.

    You can work out the first two, simply by substituting x=0, into the appropriate formula. f''(x), or f'(x).

    To find the third, f(0), we need to establish a relationship between all three, so we can form an equation, with the unknown f(0), and the two other known values.

    These three terms are the a0, a1, a2 of the AP.

    And follow my first post.
    Finally I got it. Thank you so much
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: October 7, 2017
Poll
Do you think parents should charge rent?
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.