University Level

Problem 1) (2 points): A farmer has 60 meters of fencing and wants to fence off a rectangular field that borders a straight river. The farmer needs no fence along the river. What are the dimensions of the field that has the largest area? Problem 2) (3 points): Sketch the graph of f (x) _ (1+x)- 1+x2 by following the following procedure for graphing y - f (x): 1. Identify the domain of f and any symmetries the curve may have. 2. Find the derivatives y' and y". 3. Find the critical points of f, if any, and identify the function's behav- ior at each one. 4. Find where the curve is increasing and where it is decreasing. 5. Find the points of inflection, if any occur, and determine the concavity of the curve. 6. Identify any asymptotes that may exist. 7. Plot key points, such as the intercepts and the points found in steps 3 5, and sketch the curve together with any asymptotes that exist