00:01
Here we're given the derivative of a function and we're asked for some details about the original function.
00:07
First off, where is the function increasing and where is it decreasing? well it's going to be increasing anywhere it's positive.
00:13
So that's going to be from 0 to 2 because it's above the line here.
00:17
And then it's going to happen again from 4 to 6 and then again from 8 to 9 or just let's say to infinity.
00:26
For part b, where is it negative? well that's going to be from 2 to 4 because it's below the axis.
00:30
And then again from 6 to 8.
00:32
For part c, when does f have a local maximum? well it's going to have a maximum when it goes from the derivative is positive to negative.
00:42
So we'll find our critical values of 2, 4, 8, and 6 because that's where it's undefined.
00:48
So it's going to have a local maximum when it goes positive negative...