Differentiation

Why is it that I can differentiate a function twice to determine whether I have a maximum or minimum?

Cuz the book says so?

You're not funny

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.

Cheers, slightly understand. Need to do a bit of research on that word 'Concavity'

What is this KA video called?