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Welcome back to Calculus I and welcome to
Week nine of our time together.

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Can you believe that we've been at this
for more than two months already?

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It's crazy.
The last two weeks, we've really been

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focusing on applications of the derivative
in a particular word problem.

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Right?
Those related rates problems or those

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optimization problems.
They're word problems, stories from real

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life.
This week, in week nine, we're still doing

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applications of the derivative, but it's
not so much word problems anymore.

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It's sort of numerical applications.
In particular, we're going to look at

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Newton's method, which is a way of
approximating a 0 of a function.

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And we did that a while back.
By using this bisection method and an

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intermediate value theorem but Newton's
method is, at least when it works, much

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faster.
And the other thing that we're going to

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look at is how knowing information about
the derivative lets you recover some

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numerical information about the original
function.

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So if you knew for instance the derivative
and you wanted to approximate a value of a

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function, we'll see how you can do that.
Well I hope you enjoyed these numerical

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examples.
When, when I first took calculus I got to

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say that I didn't always enjoy all the
numbers that were coming up, you know?

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I really just wanted to do all of the
theorems, you know?

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But I think the numbers really make this
subject come alive.

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So I encourage you, if you're skeptical
about all the numerical stuff this week,

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just take a look.
I think it's going to be a lot of fun.