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18.01 Single Variable Calculus, Fall 2007
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18.01 Single Variable Calculus, Fall 2007
Transcript – Lecture 12
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PROFESSOR: In the twelfth lecture, we're going to talk about maxima and minima.
Let's finish up what we did last time. We really only just started with maxima and
minima. And then we're going to talk about related rates. So, right now I want to
give you some examples of maxmin problems. And we're going to start with a fairly
basic one. So what's the thing about maxmin problems? The main thing is that
we're asking you to do a little bit more of the interpretation of word problems. So
many of the problems are expressed in terms of words. And so, in this case, we have
a wire which is length 1. Cut into two pieces. And then each piece encloses a square.
Sorry, encloses a square. And the problem  so this is the setup. And the problem is
to find the largest area enclosed.
So here's the problem. Now, in all of these cases, in all these cases, there's a bunch
of words. And your job is typically to draw a diagram. So the first thing you want to
do is to draw a diagram. In this case, it can be fairly schematic. Here's your unit
length. And when you draw the diagram, you're going to have to pick variables. So
those are really the two main tasks. To set up the problem. So you're drawing a
diagram. This is like word problems of old, in grade school through high school. Draw
a diagram and name the variables. So we'll be doing a lot of that today. So here's
my unit length. And I'm going to choose the variable x to be the length of one of the
pieces of wire. And that makes the other piece 1  x. And that's pretty much the
whole diagram, except that there's something that we did with the wire after we cut
it in half. Namely, we built two little boxes out of it. Like this, these are our squares.
And their side lengths are x / 4 and (1  x) / 4. So, so far, so good.
And now we have to think, well, we want to find the largest area. So I need a
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This note was uploaded on 01/18/2012 for the course MATH 18.01 taught by Professor Brubaker during the Fall '08 term at MIT.
 Fall '08
 BRUBAKER
 Calculus

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