MATH 1505 Study Guide - Quiz Guide: Scilab, Mean Value Theorem, Measles Virus

• School: York University
• Department: Mathematics and Statistics
• Course: MATH 1505
• Professor: Norman Purzitsky

Document Summary

Fall 2014: (10 points) find where the following functions are increasing and decreasing. (a) (5 points) f (x) = x2. Solution: f (x) = f (x) = x2. Critical points: x = 0, x = 1. 0 < x < 1 and decreasing elsewhere. (b) (5 points) g(x) = x3 3x2 9x + 4. Should pos/neg function incr/decr indicate that derivative g(x) = x3 3x2 9x + 4 g (x) = 3x2 6x 9 = 3 (x 3) (x + 1) Critical points: x = 1, x = 3. Decreasing for 1 < x < 3 and in- creasing elsewhere. Should pos/neg function incr/decr indicate that derivative. Fall 2014: (10 points) let f (x) = x2 5x + 1 on [0, 2]. Find a value, c, from the mean value. Theorem so that f (c) = f (b) f (a) Solve 2c 5 = c = Solution: f (x) = 2x5 5x4 f (x) = 10x (x 2)