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In the following exercises, solve the given maximum and minimum problems.A beam of rectangular cross section is to be cut from a $\log 2.00 \mathrm{ft}$ in diameter. The stiffness of the beam varies directly as the width and the cube of the depth. What dimensions will give the beam maximum stiffness? See Fig. 24.67.

Calculus 1 / AB

Chapter 24

Applications of the Derivative

Section 7

Applied Maximum and Minimum Problems

Derivatives

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In mathematics, precalculu…

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Logging. The width $w$ and…

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Solve.The maximum weig…

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The strength $S$ of a rect…

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Solve each problem. See Ex…

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all right, Question 30. I think we need now we have s balls, K h squared of you, and we have a diameter equals 20 inches. And we, of course, know our factory in here. Um um, Palm Beach, where plus the rooms for years equals 20. Weird, because we're dealing with a log attempt to draw this, You my love. So I'm drawing my triangle in which my hi my diameter is actually my, um, iPod news. You make that out there. So I saw my, uh, equation for H. And I get each this very, uh, negative Davies player plus 400. I'm gonna substitute that in for each in this equation. No, I had as in cool sometimes. Didn't. Kay Negative. Devon Square is actually a member radical waas 400 and squared. So the radical sign and we're gonna cancel each other out. I'm w when that I am s e equals k time. Negative use were plus 400 time W I'm gonna distribute that w may have you Q plus 400 that you Now I'm gonna take the driven, and the constant would actually stay as a constant. So I'm gonna write my derivative without the constant. But I know that the constant would still be a multiplier. So, yes, I'm sorry that zero Vero equals negative Read of use squared plus 400 and then in itself for better you negative 400 equals They negative three w square. So my signs cancel divide by three or 100 over three. It's weird that I'm only walking talking about a distance. I don't have to worry about the negative equals W spirit of 400 is 2020 over this square root of three. Gonna rationalize that denominator. And I'm gonna get 20 square root of three over three. And then I'm going too. So that was for W. Plug it back into my equation or each so I had huge. You won't negative and just gonna do you root them or 100 over three square plus 400. So this radical and the square cancel out and I have a TSH equals 400 degrees, 400 once for grand. That would be H E rooms. I won't. Every 12 hundreds have 800 100. The worst will be one times two over this food for three and we rationalize that we would get ht equal money times were six

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