00:01
Okay, here we have a graph of the derivative of a function, and we're trying to figure out things about the actual function.
00:07
First, we want to know where the function is increasing.
00:10
If a function is increasing, that means it's going to have a positive slope, a positive rate of change, and the derivative is the slope, it is the rate of change.
00:18
So we're looking for where this graph is positive, or where it's greater than zero, where it's above the x -axis.
00:28
It's above the x -axis right here, where i highlighted in yellow, and that would be from one to six.
00:34
At one and six, it's zero.
00:36
It's not positive or negative, so when we write this in interval notation, we're going to be using those round brackets for open parentheses instead of the closed brackets, because one and six don't count here.
00:48
They don't, they aren't included in that.
00:50
It's kind of the opposite for where f is decreasing.
00:53
That's where we're looking for a negative slope, and so we're below the x -axis.
01:03
It's below the x -axis, kind of on those tail ends, and it does include these endpoints right here because it's still going down at those endpoints.
01:15
So in this case, when we write the interval notation, we're going to be writing it in with some closed brackets for those endpoints...