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

    7
    ReputationRep:
    last minute question before c1 tomorrow!
    when drawing cubics, how do you know where to draw the vertex if you haven't found it out? e.g., i have the cubic x^3 + 2x^2 - 5x - 6
    ive found out the factors, so it crosses the x axis at 2, -3 and -1
    and i know how to draw the general shape of the cubic graph, but i always draw the minimum/maximum points wrong, as they have to be on a certain side of the y axis and i'm not sure how you're supposed to know where they are? any help? thanks
    Offline

    11
    ReputationRep:
    Set f'(x)=0 and solve it to find the turning points (if any) in the usual way.

    Since f(x) is a cubic, then f'(x)=0 will require that you solve a quadratic.
    • Thread Starter
    Offline

    7
    ReputationRep:
    (Original post by atsruser)
    Set f'(x)=0 and solve it to find the turning points (if any) in the usual way.

    Since f(x) is a cubic, then f'(x)=0 will require that you solve a quadratic.
    when you say f'(x) do you mean the derivative?
    Offline

    11
    ReputationRep:
    (Original post by georgiaaaxo)
    when you say f'(x) do you mean the derivative?
    Yes.
    • Study Helper
    Offline

    16
    ReputationRep:
    Study Helper
    (Original post by georgiaaaxo)
    last minute question before c1 tomorrow!
    when drawing cubics, how do you know where to draw the vertex if you haven't found it out? e.g., i have the cubic x^3 + 2x^2 - 5x - 6
    ive found out the factors, so it crosses the x axis at 2, -3 and -1
    and i know how to draw the general shape of the cubic graph, but i always draw the minimum/maximum points wrong, as they have to be on a certain side of the y axis and i'm not sure how you're supposed to know where they are? any help? thanks
    Since the coefficient of x^3 is positive, you know that when x is big and negative, then the cubic is big and negative; and when x is big and positive, the cubic is big and positive.

    So start with your pencil down below the the x axis and draw a rough cubic curve upwards till you cross the x-axis at -3; draw up to a peak somewhere between -3 and -1, then come down to cross the axis again at x=-1; then down till there's a trough (minimum) somewhere between -1 and 2, then come upwards to cross the axis at x = -1 again; then keep going upwards to indicate the general shape of the curve.

    You can differentiate to get the exact turning points if the question requires you to mark them
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: May 12, 2013
Poll
Are you going to a festival?
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.