Turn on thread page Beta

How to show a line is the tangent in a curve? watch

    • Thread Starter
    Offline

    16
    ReputationRep:
    Hey so i have just done a solomon paper where the question was

    show that the line y=8-2x is a tangent to the curve y=x2-6x+12?


    I basically equated the two gradients together e.g. -2=2x-6 to say that the line must be a tangent when x =2 but am i allowed to do this?

    In the mark scheme it equated the to equations together to say that as (x-2)^2 is a repeated root, it must be a tangent? Could someone also explain this to me?


    Thanks x
    Offline

    20
    ReputationRep:
    you do what you said to make a new quadratic equation. if this has a repeated root then the line must be a tangent to the curve.
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    Yeah you basically prove a point is on both the curve and the line which means they touch at that point, then prove the line and curve have the same gradients at that point.
    • Thread Starter
    Offline

    16
    ReputationRep:
    (Original post by the bear)
    you do what you said to make a new quadratic equation. if this has a repeated root then the line must be a tangent to the curve.
    so does the repeated root mean that the lines share the same point. Say you were not to get a repeated root, would that just mean the tangent and the curve meet twice?
    • Community Assistant
    Offline

    17
    ReputationRep:
    Community Assistant
    You can look at the intersection equation and prove there's one real root (repeated) by considering discriminant/solving
    • Thread Starter
    Offline

    16
    ReputationRep:
    (Original post by Tubbz)
    Yeah you basically prove a point is on both the curve and the line which means they touch at that point, then prove the line and curve have the same gradients at that point.
    okay thank you!!!! I dont know whether to give myself marks as my entire answer was:

    If the line is a tangent to the curve, they would share the same gradient" then obviously i found x =2.

    This is alevel ocr btw
    Offline

    20
    ReputationRep:
    (Original post by Appazap)
    so does the repeated root mean that the lines share the same point. Say you were not to get a repeated root, would that just mean the tangent and the curve meet twice?
    yes; the line would then form a "secant".

    if the quadratic had no roots then the line would miss the curve completely.
    Offline

    16
    ReputationRep:
    you do 8-2x=x^2-6x+12 and find the solution.
    If it is a tangent it should only have one root as it cuts the curve at one point.
    • Thread Starter
    Offline

    16
    ReputationRep:
    (Original post by aceplayyt)
    you do 8-2x=x^2-6x+12 and find the solution.
    If it is a tangent it should only have one root as it cuts the curve at one point.
    hmmn how many marks do you think my working ou got for that question, it was 4 marks?
    Offline

    16
    ReputationRep:
    (Original post by Appazap)
    hmmn how many marks do you think my working ou got for that question, it was 4 marks?
    Dunno what you meant by -2=2x-6

    but I guess upto working out x=2 would be about 3 marks then saying it is a tangent due to there being 1 root would be the 4th mark
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: February 21, 2018

University open days

  • University of Exeter
    Undergraduate Open Days - Exeter Campus Undergraduate
    Wed, 24 Oct '18
  • University of Bradford
    Faculty of Health Studies Postgraduate
    Wed, 24 Oct '18
  • Northumbria University
    All faculties Undergraduate
    Wed, 24 Oct '18
Poll
Who is most responsible for your success at university
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.