00:01
Okay, so we're given y equals 5x squared plus natural log of x, where x is bigger than 0.
00:08
We're going to find where this function is concaving up and down.
00:12
That means we need some derivatives.
00:13
Let's start with the first here.
00:15
The first derivative is 10x plus 1 over x.
00:19
The second derivative, which is what we need, is going to be 10 minus 1 over x squared.
00:26
We note that x equals 0 means that we have a, does not exist, or discontinuity.
00:31
It doesn't matter though, because x equals 0 is not within our domain.
00:35
Now we're just going to set this equal to 0 and solve.
00:38
So i get 1 over x squared equals 10.
00:41
So 1 equals 10x squared, or 1 tenth equals x squared.
00:46
So x is going to be just root 1 over 10.
00:51
And i'm not going to consider the plus or minus, just the plus, because negative would be less than 0...