Learning How to Use the Prime G2 - Hallway Pole Problem - In Three Parts
09-04-2019, 12:53 AM (This post was last modified: 09-04-2019 01:13 PM by Albert Chan.)
Post: #6
 Albert Chan Senior Member Posts: 2,625 Joined: Jul 2018
RE: Learning How to Use the Prime G2 - Hallway Pole Problem - In Three Parts
(09-02-2019 11:32 PM)jlind Wrote:

Differentiating the Pythagorean equation using the "chain rule":

c' = f'(x) = (1/2)*((x+5)^2 + (10 + 50/x)^2)^(-1/2) * 2(x+5) + 2*(10 + 50/x)*(-1)*(50/x^2)

Don't think I want to try to find the root to this one . . .

Nice post.

To minimize c, you just need to minimize c^2
(Actually, it does not matter. c' = (c^2)' / (2c))

$$\large (c^2)'= 2(x+5) + 2(10+ {50 \over x})({-50 \over x^2}) = 2(x+5) - {1000(x+5) \over x^3} = { 2(x+5) (x^3-500) \over x^3}$$

$$\large (c^2)'=0 → x = 5 \sqrt[3]4 ≈ 7.93701$$

$$\large \min(c) = 5(1+ \sqrt[3]4)^{3/2} ≈ 20.80969$$
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 Messages In This Thread Learning How to Use the Prime G2 - Hallway Pole Problem - In Three Parts - jlind - 09-02-2019, 11:32 PM Learning How to Use the Prime G2 - Hallway Pole Problem - Part II of III - jlind - 09-02-2019, 11:38 PM Learning How to Use the Prime G2 - Hallway Pole Problem - Part III of III - jlind - 09-02-2019, 11:42 PM RE: Learning How to Use the Prime G2 - Hallway Pole Problem - In Three Parts - teerasak - 09-03-2019, 07:23 AM RE: Learning How to Use the Prime G2 - Hallway Pole Problem - In Three Parts - JoJo1973 - 09-03-2019, 06:00 PM RE: Learning How to Use the Prime G2 - Hallway Pole Problem - In Three Parts - jlind - 09-04-2019, 02:42 AM RE: Learning How to Use the Prime G2 - Hallway Pole Problem - In Three Parts - Albert Chan - 09-04-2019 12:53 AM RE: Learning How to Use the Prime G2 - Hallway Pole Problem - In Three Parts - teerasak - 09-04-2019, 04:10 AM RE: Learning How to Use the Prime G2 - Hallway Pole Problem - In Three Parts - jlind - 09-04-2019, 09:17 AM RE: Learning How to Use the Prime G2 - Hallway Pole Problem - In Three Parts - jlind - 09-12-2019, 04:03 PM RE: Learning How to Use the Prime G2 - Hallway Pole Problem - In Three Parts - teerasak - 09-13-2019, 04:16 PM RE: Learning How to Use the Prime G2 - Hallway Pole Problem - In Three Parts - Thomas Klemm - 07-12-2022, 12:29 AM RE: Learning How to Use the Prime G2 - Hallway Pole Problem - In Three Parts - jte - 08-12-2022, 10:07 PM

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