Welcome back to Calculus I and welcome to Week nine of our time together.
Can you believe that we've been at this for more than two months already?
It's crazy. The last two weeks, we've really been
focusing on applications of the derivative in a particular word problem.
Right? Those related rates problems or those
optimization problems. They're word problems, stories from real
life. This week, in week nine, we're still doing
applications of the derivative, but it's not so much word problems anymore.
It's sort of numerical applications. In particular, we're going to look at
Newton's method, which is a way of approximating a 0 of a function.
And we did that a while back. By using this bisection method and an
intermediate value theorem but Newton's method is, at least when it works, much
faster. And the other thing that we're going to
look at is how knowing information about the derivative lets you recover some
numerical information about the original function.
So if you knew for instance the derivative and you wanted to approximate a value of a
function, we'll see how you can do that. Well I hope you enjoyed these numerical
examples. When, when I first took calculus I got to
say that I didn't always enjoy all the numbers that were coming up, you know?
I really just wanted to do all of the theorems, you know?
But I think the numbers really make this subject come alive.
So I encourage you, if you're skeptical about all the numerical stuff this week,
just take a look. I think it's going to be a lot of fun.