Practice Test 4 This is a practice test only, do not expect the test to look exactly like this. Problem 1. What are the dimensions of a rectangle whose perimeter is 100 units and whose area is as large as possible. Problem 2. What are the dimensions of a rectangle whose arca is 1000 square units and whose perimeter is as small as possible. Problem 3. A farmer wants to fence in a rectangular pasture of 1.5 million square feet and then divide the pasture in half with a fence parallel to the sides of the rectangle. How can this be done in such a way as to minimize the amount of fencing required? Problem 4. A piece of wire 10 meters long is to be cut into two pieces. One piece will be bent into a perfect circle the other piece into an equilateral triangle. Where should the cut be made so that the resulting figures have the maximum possible combined area? Problem 5. A fence 8 feet tall runs parallel to a building at a distance 4 feet from the building. What is the shortest ladder that will reach over the fence to the building? Problem 6. Find the antiderivative for each of the following functions. 1. f(x) = 613 - 8x1 + 915 2. f (t ) = tz - 8tz + ex 3. f(x) = 2sin (x) - VI+ 4. f (t) = t - 3 5. f(s) =2* - 3sec (s) tan (I) Problem 7. If f'(x) = sin (r) - cos (x) and f(0) = 3 find f(I) Problem 8. If f"(x) = ex - 2 sin (r), f(0) = 3 and f'(7 = 0 find f(2) Problem 9. Estimate the area under the curve f(r) = sin (x) from 2 = 0 to r = 5 using 4 subintervals and a right hand sum. Repeat this but use a left hand sum. Problem 10. Estimate the upper and lower sums for the curve f(r) = 2 + sin (x) from I = 0 to x = 7 using 10 sub-intervals and a right hand sum. Repeat this but use a left hand sum