Learning How to Use the Prime G2 - Hallway Pole Problem - In Three Parts

[Albert Chan]

(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))

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

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

\(\large \min(c) = 5(1+ \sqrt[3]4)^{3/2} ≈ 20.80969 \)