This has the undesired effect of having the longest distance of all, probably ensuring a nonminimal cost. The optimal solution likely has the line being run along the ground for a while, then underwater, as the figure implies. We need to label our unknown distances: the distance run along the ground and the distance run underwater. Recognizing that the underwater distance can be measured as the hypotenuse of a right triangle, we can label our figure as follows {{CMD_134}} {{ENV_135}} {{CMD_136}} By choosing {{MATH_137}} as we did, we make the expression under the square root simple. We now create the cost function: {{MATH_138}} So we have {{MATH_139}} This function only makes sense on the interval {{MATH_140}}. While we are fairly certain the endpoints will not give a minimal cost, we still evaluate {{MATH_141}} at each to verify. {{MATH_142}} We now find the critical points of {{MATH_143}}. We compute {{MATH_144}} as {{MATH_145}} Recognize that this is never undefined. Setting {{MATH_146}} and solving for {{MATH_147}}, we have: {{ENV_148}} Evaluating {{MATH_149}} at {{MATH_150}} gives a cost of about {{MATH_151}}. The distance the power line is laid along land is {{MATH_152}} and the underwater distance is {{MATH_153}}. {{CMD_154}} We can confirm our results by looking at the graph of {{MATH_155}}: {{MATH_156}} {{CMD_157}} {{CMD_158}} {{CMD_159}}