You are Here: Home >< Maths

# Second derivative is 0 at a minimum point? Watch

Announcements
1. What does it mean when the second derviative is 0 at a minimum or maximum point? Why isn't it positive or negative?
2. (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
3. (Original post by IYGB)
Possibly a point of inflexion
No it is not. Consider: y= x^4
4. (Original post by Rana1997)
No it is not. Consider: y= x^4
I never said it was. I said possibly
5. (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?
6. (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.
7. (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.
8. (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.
9. (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].

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: October 3, 2016
Today on TSR

### How would you do in an Oxford interview?

Put yourself through the test

### STI without any sexual activity?

Discussions on TSR

• Latest
• ## 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
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## 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

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.