Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    11
    ReputationRep:
    The curve of f(x) = ax^2 + bx + c passes through the point (2, 24) and the gradient of the curve at this point is 22.
    The value of f''(x) is 6.
    Find the coordinates of the points where the curve crosses the x-axes and y-axes and of the minimum stationary point.
    Offline

    0
    ReputationRep:
    Put in 2 and 24. That gives you one equation for a,b,c

    Differentiate, put in 2 and 22, and that gives you an equation for a and B

    Differentiate again , put in 2 and 6 for the values and a falls straight out.

    Once you have a,b and c, it is easy to find the intercepts and the stationary point.
    Offline

    0
    ReputationRep:
    f(2): 

\Rightarrow 24=4a+2b+c

    f'(x)=2ax+b
    f'(2):

\Rightarrow 22=4a+b

    f''(x)=2a
    \Rightarrow 6=2a
    \therefore a=3

    22=12+b
    \therefore b=10

    24=12+20+c
    \therefore c=-8

    Hence
    f(x)=3x^2+10x-8

    Y-Int: Let x=0
    f(0)=-8
    Therefore, y-int is (0,-8)

    X-Int: When f(x)=0
    0=(x+4)(2x-3)
    x=-4orx=\frac{2}{3}
    Therefore, x-ints occur at (-4,0) and (\frac{2}{3},0)

    f'(x)=6x+10
    For stationary pts, let f'(x)=0
    0=2(3x+5)
    x=\frac{-5}{3}

    f(\frac{-5}{3})=\frac{-49}{3}
    Therefore, stationary point occurs at (\frac{-5}{3}),\frac{-49}{3})

    Hehehe. I was bored so i decided to post this up. =]
 
 
 
  • 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
    Would you like to hibernate through the winter months?
    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.