MATH 4060 Final: MATH 4060 Iowa 2016OldFinalquestions
Document Summary
This exam is over the material in chapter 4 and sections 5. 1, 5. 2, 5. 4 and 5. 5. Study this review, the material for quiz 4,quiz 5, quiz 6 and the appropriate homework as- signments. Then check your answers against the solutions: properties of graph: intervals of concavity, rst and second derivative tests. Take the rst derivative. f (x) = 200x199 200. Find the critical numbers: 200x199 200 = 0 to nd x = 1. ( the only real root. ) Find the second derivative. f (x) = (200)(199)x198. (a) find the sign for f f . The sign of f is positive everywhere. So the function is concave upward on all values of x. (b) put the critical number on the number line above to use the second derivative test. f . The value of f at the critical number is positive ( smiley face) and f has a relative minimum at x = 1.
