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Problem 69

A point $P$ needs to be located somewhere on the line $AD$ so that the total length $L$ of cables linking $P$ to the points $A$, $B$, and $C$ is minimized (see the figure). Express $L$ as a function of $x = | AP |$ and use graphs of $L$ and $dL/dx$ to estimate the minimum value of $L$.

$$9.35 \mathrm{m}$$

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## Video Transcript

we're trying to figure out the minimum value. Al. It's the first thing is remember, the Pythagorean theorem is a squared plus B squared equals C squared. Well. In this context, we know this could help us find the driven of opium. Axe is one plus X minus five over squared of X squared minus 10 acts lost 29 plus X minus five over squared of X squared minus 10 acts plus 34. The minimum value has reached it approximately 9.35 meters. See, this is approximately 3.59