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# P24 - point on the graph to the point where the bird is...

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Project 24 MAC 2233 1. (From lecture) You are required to construct a closed rectangular box with a surface area of 48 square feet so that the length is twice the width. What dimensions will maximize the volume of the box? 2. Sketch the graph of the function f ( x ) = 4 x on the interval [ 0 , 16 ] . Shade the region between the x -axis and the curve on your interval. Assume that the axes measure distance in hundreds of feet. Suppose the shaded region is a marsh and the ivory-billed woodpecker is perched on a stump in the lake at position ( 8 , 4 ) . Draw it on the graph as well. In terms of x alone, any generic point on the graph of f ( x ) has coordinates: ( x , ) Hoping for a prize picture of the supposedly extinct bird, you quickly calculate the position at the edge of the lake (the point on the graph) closest to the bird. What are the coordinates of this point? Note that you are finding the SHORTEST possible DISTANCE from your generic

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Unformatted text preview: point on the graph, to the point where the bird is perched. 3. Recall the following problem from the text and Exam 1: A company wishes to run cable from an island 6 miles from shore to a power station 10 miles from point P on the shore directly across from the island; Suppose the cost of laying the cable on land is \$ 2000 per mile, and the cost of laying the cable underwater is \$ 3000 per mile. Suppose the company decides to run the cable from the island to the point A (between the station and point P ), and then from point A to the station. a) As before, write a formula for the function C ( x ) , representing the total cost of laying out the cable. What is its domain? b) Show that x = 12 √ 5 will result in the minimum total cost of laying out the cable....
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P24 - point on the graph to the point where the bird is...

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