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hw9-30 - x sin(2 x(b f x = 1 √ 2 csc x cot x Hints and...

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Math 170-007 Homework 9/30 Fall 2010 1. Compute the derivative for each of these functions. (a) f ( x ) = sin(4 x ) (b) f ( x ) = e 3 x (c) f ( x ) = cos parenleftBig πx 2 - π 4 parenrightBig (d) f ( x ) = 1 . 3 e 0 . 2 x sin(12 . 5 x - 3 . 7) 2. From Schaum’s Outline , Chapter 10: 32-45 all. 3. From the Online Textbook, Section 3.5: 36-39 all. 4. For each of the following functions, locate all horizontal tangents in the domain 0 x π . Then graph each function to confirm your answer. (Bumps in the graph should match up with your locations for horizontal tangents.) (a) f
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Unformatted text preview: x + sin(2 x ) (b) f ( x ) = 1 + √ 2 csc x + cot x Hints and Answers 1. (a) f ′ ( x ) = 4 cos(4 x ) (b) f ′ ( x ) =-3 e − 3 x (c) f ′ ( x ) =-π 2 sin p πx 2-π 4 P (d) f ′ ( x ) = 1 . 3(-. 2) e − . 2 x sin(12 . 5 x-3 . 7) + 1 . 3 e − . 2 x (12 . 5) cos(12 . 5 x-3 . 7) or f ′ =-. 26 e − . 2 x sin(12 . 5 x-3 . 7) + 16 . 25 e − . 2 x cos(12 . 5 x-3 . 7). 4. (a) x = π/ 3 and 2 π/ 3 (b) x = 3 π/ 4...
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