00:01
Here we're given a function and we're asked to identify where the function is concave up and concave down.
00:06
So f of x will be x to the fourth minus 3x cubed plus 3.
00:11
So concavity is defined by the second derivative.
00:14
So let's take the first derivative so that we can take the second.
00:17
This is a power rule so we have 4x cubed minus 9x squared.
00:22
And then we actually need the second derivative.
00:24
So let's do the second derivative is another power rule.
00:27
So we have 12x squared minus 18x.
00:32
And we want to set that equal to zero.
00:35
So i can pull out a 3 and an x.
00:39
I'm left with 4x minus 6.
00:44
I guess i could have pulled out a 6 actually.
00:46
Oh well, doesn't really matter.
00:47
We get x equals 0.
00:50
And we can also get 4.
00:51
That's not an x...