2 2. A power line is to be constructed from the shore of a lake to an island that is 1 km away. A power source S is 4 km along the shore from a point P on the shore that is closest to the island. Suppose it costs 3 thousand dollars per km to lay the power line along the shore, and 5 thousand dollars per km to lay the cable under water. Island 1 km LAKE Power PE > S 4 km (a) Let C(x) be the total cost (in thousands) of laying the power line when the junction of the shore power line and the under-water power line is a distance x km from P. Find C(x) (b) The derivative of C(x) is C'(x) =- 5x - 3. Vx2 + 1 Solve C'(x) =0 to find the distance x from P to the junction so that cost will be minimized