Deriviate Calculus 251

Math 251 Test 3. (CHANGE ALL PROBLEMS) 1. Find and classify (local max, local min or inflection point) the critical points of the following functions: f(x) = x2 x + 1 2. Find the absolute maximum and absolute minimum of the following function on the given interval f(x) = x3 - 6x2 + 9x + 2, [-1, 4] 3. Find the absolute maximum and absolute minimum of the following function on the given interval f(x) = 3x2 - 12x + 5, [0, 3] 4. Find the linearization of the following functions at the given points. f(x) = x2 + x at x = 2. 5. Use linear approximation to estimate the following (no calculator of course): p26 6. Find the positive number x such that the sum of x and twice its reciprocal is as small as possible. 7. One side of an open field is bounded by a straight river. What are the dimensions needed for a fence around the other three sides of a rectangular plot in order to enclose as great an area as possible given that you have 1000 feet of fence? 8. A poster is to contain 100 square inches of printed matter (the picture part) with (blank) margins of 3 inches each at the top and bottom and 4 inches on each side. Find the dimensions (outer dimensions of the entire poster with picture and margins) if the total area of the poster (margins included) is to be a minimum. 9. A closed rectangular container with a square base is to have a volume of 2000 cubic centimeters. It costs twice as much per square centimeter for the top and bottom as it does for the sides. Find the dimensions of the container of least cost.