Hey there! Sign in to join this conversationNew here? Join for free

Second derivative is 0 at a minimum point? Watch

Announcements
    • Thread Starter
    Offline

    1
    ReputationRep:
    What does it mean when the second derviative is 0 at a minimum or maximum point? Why isn't it positive or negative?
    Offline

    3
    ReputationRep:
    (Original post by Rana1997)
    What does it mean when the second derviative is 0 at a minimum or maximum point? Why isn't it positive or negative?
    Possibly a point of inflexion
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by IYGB)
    Possibly a point of inflexion
    No it is not. Consider: y= x^4
    Offline

    3
    ReputationRep:
    (Original post by Rana1997)
    No it is not. Consider: y= x^4
    I never said it was. I said possibly
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by IYGB)
    I never said it was. I said possibly
    All right. But what does that mean? Why is the gradient not changing while it is supposed to be?
    Offline

    3
    ReputationRep:
    (Original post by Rana1997)
    All right. But what does that mean? Why is the gradient not changing while it is supposed to be?
    If I remember well

    Second derivative = zero AND third derivative = non zero, implies a point of inflexion.

    Second derivative = zero AND third derivative = zero, implies the second derivative test fails and a different method must be used.
    Offline

    1
    ReputationRep:
    (Original post by Rana1997)
    All right. But what does that mean? Why is the gradient not changing while it is supposed to be?
    It just means that when the line is at x=0 then the line is momentarily flat.
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by YouHaveProblems)
    It just means that when the line is at x=0 then the line is momentarily flat.
    That is when the first derivative is 0. The second derivitive is the change in the gradient which also becomes 0. This will make sense at an inflection point but it is illogical for minima and maxima.
    Offline

    17
    ReputationRep:
    (Original post by IYGB)
    If I remember well

    Second derivative = zero AND third derivative = non zero, implies a point of inflexion.

    Second derivative = zero AND third derivative = zero, implies the second derivative test fails and a different method must be used.
    Well, even in the first case the "second derivative test" has failed, since you are needing to look at the 3rd derivative as well.
    If 2nd and 3rd. More generally, if the 1st, 2nd, ..., nth derivatives are zero but the n+1st is not, then if n is even we have a point of inflexion, if n is odd we have a maximum if the n+1st derivative is -ve, a minimum otherwise.

    Note, however that it is possible for a (real) function to be infinitely differentiable and have a maximum point where all derivatives are zero.

    (Original post by Rana1997)
    That is when the first derivative is 0. The second derivitive is the change in the gradient which also becomes 0. This will make sense at an inflection point but it is illogical for minima and maxima.
    Slight correction: the second derivative is the rate of change in the gradient. It's perfectly possible for the rate of change in the gradient to be zero at a maxima / minima. [Compare with the fact that the first derivative can be zero at a point without the function having to be constant there].
 
 
 
  • 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
    Break up or unrequited love?
    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.