x Turn on thread page Beta
 You are Here: Home >< Maths

# Differentiation watch

1. Why is it that I can differentiate a function twice to determine whether I have a maximum or minimum?
2. (Original post by NinCheng)
Why is it that I can differentiate a function twice to determine whether I have a maximum or minimum?
Cuz the book says so?
3. (Original post by M14B)
Cuz the book says so?
You're not funny
4. (Original post by NinCheng)
You're not funny
Do you have to dent my confidence?
5. (Original post by NinCheng)
Why is it that I can differentiate a function twice to determine whether I have a maximum or minimum?
Technical reason: because it gives information on concavity.

Here's a picture that sums it up:

But basically, if the second derivative is negative, that means your gradient is just going to get shallower and shallower since the gradient is then a decreasing function, so the function will decrease since the gradient is getting shallower hence that point is a maximum.

If the second derivative is positive, that means your gradient is getting steeper and steeper and hence the function will only grow from there, hence it's a minimum.
6. (Original post by Zacken)
Technical reason: because it gives information on concavity.

Here's a picture that sums it up:

But basically, if the second derivative is negative, that means your gradient is just going to get shallower and shallower since the gradient is then a decreasing function, so the function will decrease since the gradient is getting shallower hence that point is a maximum.

If the second derivative is positive, that means your gradient is getting steeper and steeper and hence the function will only grow from there, hence it's a minimum.
Cheers, slightly understand. Need to do a bit of research on that word 'Concavity'

What is this KA video called?
7. (Original post by NinCheng)
Cheers, slightly understand. Need to do a bit of research on that word 'Concavity'

What is this KA video called?
Here you go.

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: April 12, 2016
Today on TSR

### I've studied the wrong subject

...Should I go back to school?

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