[music]. Welcome back to Calculus One, and welcome
to week eight of our time together. Last week, during week seven, we began
studying applications of the derivative and we focused in on related rates
problems. It's not so surprising, I think that
calculus can solve these related rates problems.
After all calculus is all about how things change, so it makes sense that you could
use calculus to study how things are changing together.
This week, in week eight, we focus on optimization problems.
Optimization problems are all about the best of something, right?
You want to find the shape of a soup can that maximizes the amount of soup for a
given amount of metal. Or you want to find the shape of
rectangular fence that encloses the most area for a given length of fence.
Or you want to find the shape of rectangular fence that encloses the most
area for a given length of fence. Or you want to understand why bubbles form
the shapes that they do or why light travels on the paths that it does.
Right? All of these are problems about finding
the best of something and that's really different in related rates problems.
Right? We're not just asking about how something
changes, I'm actually trying to find a point where some function achieves a
maximum or a minimum value. And I think it is really surprising that
calculus, which fundamentally, is all about how things change can also be used
to solve that problem. It can also be used to find a specific
value or something really exiting happens. I also want to say thank you.
It's is a long and difficult course, and you've made it now, more than half way
through. Congratulations.