00:01
For this problem, we are told that the given figure, or the figure shows the graph of the derivative f prime of x of a given function f of x.
00:10
In part a, we're asked, on what intervals is f increasing or decreasing? we have that it's going to be increasing when f prime is greater than zero.
00:19
So we can see that that would be increasing.
00:25
That would be on the interval between negative 2 and 0, union with the interval from 4 of 3.
00:33
To it would seem from 4 to infinity.
00:36
Then for decreasing, that would be when it's less than zero.
00:41
So it seems like we're coming in from negative infinity, up to negative 2, union with the interval from 0 to 2, union with the interval from 2 to 4.
00:55
Then for part b, we're asked, for what values of x does f have a local maximum or minimum? so we'd have a local maximum when we go from increasing to decreasing and a local minimum when we do vice versa.
01:09
So we would have maxima when we are at x equals zero because we go from from positive to negative.
01:23
And that would appear to be the only maximum.
01:26
We would have local minimum or minima when we swap from decreasing to increasing.
01:33
So we can see that that occurs at negative two and at four.
01:39
Then we can see that, for part c, we're asked to sketch the graph of f double prime of x.
01:44
So what i'll do is i'll just create that on the existing graph.
01:49
So we can see that overall this looks a little bit like a combination of a whole bunch of different roughly parabolic shapes...