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Suppose the box in Example 8 is to have a top as well. Determine its dimensions.

$$(6,11)$$

Calculus 3

Chapter 6

An Introduction to Functions of Several Variables

Section 3

Extrema

Partial Derivatives

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Lectures

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

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01:08

If an open box is made fro…

If an open box is made f…

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05:00

point) An open box is to b…

06:10

You are planning to make a…

03:13

Minimizing the Surface Are…

01:52

Dimensions of a Box A box …

01:02

By cutting away identica…

By cutting away identical …

we have another one of those box problems. Um So we're going to go back to what we have before Which is the volume and in this case it's going to be an 8" square and we're going to be cutting Are identical square. So that's actually even simpler because now it's going to be eight x 8. And then so we have eight minus two X. Times eight minus two X. And then times X. Because that's going to be the height of the box. Um So the dimensions of the largest box or at least the one that holds the most volume, It's gonna be right here at 1.333. So that means that our see value the height actually we can call it is going to be 4/3. And then if we plug this in for A. And B. Or the length and the width, we see that since it's a square, the length and the width are going to be the same, so length and width are going to equal 16/3. That's going to be our final answer. And we can also determine what the actual volume is going to be by multiplying this um time 16 3rd that's going to be the final volume

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