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## Homework Statement

A new cottage is built across the river and 300 m downstream from the nearest telephone relay station. The river is 120m wide. In order to wire the cottage for phone service, wire will be laid across the river under water, and along the edge of the river above ground. The cost to lay wire under water is $15 per m and the cost to lay wire above ground is $10 per m. How much wire should be laid under water to minimize cost?

## Homework Equations

[itex] a^2 + b^2 = c^2 [/itex]

## The Attempt at a Solution

[itex] C = 15\sqrt{x^2+14400} + 10(300-x) [/itex]

[itex] C' = 15 \cdot (\sqrt{x^2+14400})' - 10 [/itex]

[itex] = 15 \cdot \frac{1}{2\cdot\sqrt{x^2+14400}} \cdot(x^2+14400)' -10 [/itex]

[itex] = \frac{15\cdot (x^2)'} {2\cdot\sqrt{x^2+14400}} -10 [/itex]

[itex] = \frac{15\cdot2x}{2\cdot\sqrt{x^2+14400}} -10 [/itex]

[itex] = \frac{15x}{\sqrt{x^2+14400}} -10 [/itex]

I'm just wondering if someone can look this over and let me know where I'm going wrong? I proceeded to solve for f'(x) = 0 and I'm getting 10.7, so I know I'm doing something wrong.

I apologize for the use of ' for prime (this was how I was taught in the lesson).

Thank you very much for your time.