Please help me with these problems and show clear work.

Objectives: 1. Develop an understanding of how the derivative can be used in various situations. 2. Develop an understanding of the graphical interpretations of the derivative. ate system, sketch a graph of y = f'(x) Statement of Project: A common problem encountered by the oil industry is determining the most cost effective pipeline route in connecting various wells in an oil fertile area. The attached map is a section of a U. S. Geological Survey Contour Map of Southern Ohio with wetlands (swamp) area outlined for clarity. An existing oil well is located approximately at the point B. If a new well is dug at point A , a pipeline installation company must be directed as to where to lay connecting pipe. In consultation with the installation company, the following information has been obtained: a) Straight, two-inch coated pipe must be used at a cost of $1.50/ foot. b) A maximum of two elbow joints may be used. Assume that the elbow joints may be fabricated with any angle measure. c) In crossing normal terrain, installation is $1.20/foot. d) Installation in wetland area requires an additional Track Hoe at a cost of $60/hour. e) In a 10 hour day, a Track Hoe can dig an approximately 300 feet of ditch. Determine the pipeline route connecting the two wells at A to B which incurs the least cost. Suggestions: First solve the problem as if the wetland separating A and B were a rectangle, then improve on this solution by modeling the wetland area more accurately. Also reduce the number of paths to consider before you begin modeling. For example, one need not consider a path around the swamp area to the north since it is further that the path around the swamp to the north since it is further than the path to the south and both traverse only normal terrain. Problems for Student Investigation N 1-690 scale: 1 cm = '100 ft ROAD