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# Differentiation

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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.

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