[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.