00:01
We'll be using the second derivative test for extrema to find our local extrema, local minimums and local maxims.
00:10
First, we do need to determine our critical points.
00:13
So let's take the derivative of our current function.
00:17
We have an e to the u, and the derivative of e to the u is e to the u, du.
00:24
Now, the du is negative 2x, which i will just put in front.
00:29
And that is equivalent to negative 2x over e to the negative x squared.
00:38
For your critical points, that would be any place where that derivative is equal to zero or where it is non -differentialable.
00:47
Well, it's never non -differentiable because that should be a positive power.
00:52
The bottom can never be zero.
00:54
E to any power can only be positive.
00:58
So the only thing we really need to look at is when this fraction is zero, and a fraction is zero if the top is zero, which will occur at the x value of zero.
01:12
Now that we have determined the critical point, let's take a look at the second derivative.
01:19
And i'm going to take the derivative from here, which would use the product rule...