
Extremas
Find extrema
Answers are and 0 for x values,
Local minimas are
Which makes complete sense if you look at the graph, however algebraically I solve for local maxima (0,4) which makes no sense to me as its undefined on the graph, why does my book say it counts as a local maxima if its "undefined"?

Re: Extremas
We are given:
and we find:
So, we see we have the 3 critical values:
While the derivative is undefined for , the function is defined there, indicating we have cusps at these points.
We then find on the intervals:
derivative is negative, function is decreasing.
derivative is positive, function is increasing.
derivative is negative, function is decreasing.
derivative is positive, function is increasing.
So, by the first derivative test for extrema, we find minima at:
and a maximum at .