00:04
We're asked to figure out where is this function x cubed plus 5x squared minus 8x plus 1.
00:08
Where is it increasing? we should kind of have an idea about what cubic functions look like.
00:13
It's a positive coefficient.
00:16
So it goes up and then it goes back down and then it goes back up.
00:19
That's the general shape for a cubic when we're adding, subtracting some x squared, other xs from it.
00:24
So we can kind of see that we're going to get these two points.
00:28
It's going to be increasing from negative infinity until that first one where we have a relative maximum value.
00:34
It's going to be decreasing between that maximum, that relative maximum, and the minimum, and then it's going to be increasing forever after that minimum value there.
00:45
All right.
00:46
So if we're able to use calculus, we would find its instantaneous rate of change, find its derivative, and get 3x squared plus 10x minus 8, and then we'd see where is that undefined or equal to zero to figure out its critical values.
01:04
All right, so this is 3x and x, and we need factors of negative 8.
01:10
Now, when we put them together, give us a positive 10.
01:12
Well, that's going to be a positive 4 times 3...