A4_W2016.pdf - DISTANCE EDUCATION MATH 1500 WINTER TERM...

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DISTANCE EDUCATION MATH 1500 WINTER TERM 2016: D01/D02 Assignment 4 Sections 4.1, 4.2, 4.3, 4.5. Total Marks: 60 Due Date: Mar 6, 2016 . SHOW ALL WORK to get full marks. 1
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1. Find the critical numbers of the function. (a) [3] f p x q “ 15 x 3 ` 12 x 2 ` 3 x. (b) [3] g p t q “ | 2 t ´ 6 | 2. [5] Find the absolute maximum and absolute minimum values of f on the given interval. Justify your answer. f p x q “ 3 x 2 { 3 ´ 2 x, 1 , 1 s . 3. [6] Verify that the following function satisfies the hypotheses of the Mean Value Theorem on the given interval. Then find all numbers c that satisfy the conclusion of the Mean Value Theorem. f p x q “ 2 x 3 ` x ´ 3 , 1 , 0 s . 4. Consider f p x q “ 1 x 3 ´ 4 x . Note then that f 1 p x q “ 4 ´ 3 x 2 x 2 p x 2 ´ 4 q 2 and f 2 p x q “ 4 p 3 x 4 ´ 6 x 2 ` 8 q x 3 p x 2 ´ 4 q 3 . (a) [2] Find the domain of the function. (b) [2] Find the x and y coordinate(s) of the critical numbers. (c) [4] Find all vertical asymptote(s) of f p x q . (Show all your work).
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