00:01
Here, we're given the graph of the derivative of a function, and we're asked where the original function has a max or min.
00:08
And we're also asked for where it's increasing and decreasing, but that's really part of finding the max and mins.
00:15
So if you think about the first derivative test, and if we were to give you some function f of x, your first step is find the critical values.
00:22
That's going to be where the derivative is equal to zero.
00:25
Well, we were given the derivative instead of the function.
00:28
So that's going to be where the derivative is equal to zero right here.
00:32
So my critical values are five and nine.
00:37
Now, if we were doing this using the first derivative test, we'd do a number line, say five and nine, and we'd need to choose values in those regions.
00:47
Well, normally i'd plug in a point and plug that into the function.
00:50
But instead, let's just look at the original function.
00:54
Because i can say that right here, the function is negative, and also over here.
01:01
Sorry, the derivative is negative.
01:03
And right here, the derivative is positive...