You are vacationing at a cabin located at the point (1, 4). A river runs directly along the line y = 2x near the cabin. We want to minimize the distance we must walk from the cabin to the river. The units are in miles. See the figure.

a. Find the function D(x) that can be used to find the optimal value in this problem. Your function should depend only on the variable x.

b. Use calculus and your function D(x) from part (a) to find the coordinates (x, y) of the point on the river that minimizes the distance to the cabin.

Image transcriptions

6. You are vacationing at a cabin located at the point (1. 4). A river runs directly along the line y = 2r near the cabin. We want to minimize the distance we must walk from the cabin to Cabin the river. The units are in miles. See the figure. This problem extends to the next page. Be sure to complete both parts (a) and (b)!

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