hw-5 - Homework 5 MA 123 A2 Summer I 2010 Be rst to report...

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Homework 5 MA 123 A2, Summer I 2010 Be first to report a math error for extra credit. Read Stewart sections 3.1-3.7. Alternatively, read Basics of Differenti- ation at http://en.wikibooks.org/wiki/Calculus/Differentiation . Both sources contain ample selections of practice exercises. Exercise 1. Differentiate the function f ( x ) = 2 x - 3 / 4 . [ - 3 2 x - 7 / 4 ] Exercise 2. Differentiate the function y ( x ) = x 2 + 4 x + 3 p x . [ 3 2 p x + 2 p x - 3 2 x p x ] Exercise 3. Find a second degree polynomial p ( x ) such that p ( 2 ) = 5, p 0 ( 2 ) = 3, and p 00 ( 2 ) = 2. [ x 2 - x + 3 ] Exercise 4. Find the points on the curve y ( x ) = 2 x 3 + 3 x 2 - 12 x + 1 where the tangent line is horizontal. [ ( - 2,21 ) , ( 1, - 6 ) ] Exercise 5. Differentiate the function e x x 2 . [ ( x - 2 ) e x / x 3 ] Exercise 6. Differentiate the function g ( x ) = 3 x - 1 2 x + 1 . [ 5 / ( 2 x + 1 ) 2 ] Exercise 7. Differentiate the function x 3 1 - x 2 . [ x 2 ( 3 - x 2 ) ( 1 - x 2 ) 2 ] 1
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2 Exercise 8. Differentiate the function A B + Ce x . [ - ACe x / ( B + Ce x ) 2 ] Exercise 9. Find f 0 ( x ) and f 00 ( x ) if f ( x ) = x 4 e x . [ ( x 4 + 4 x 3 ) e x , ( x 4 + 8 x 3 + 12 x 2 ) e x ] Exercise 10. Plot the curve y ( x ) = x / ( x + 1 ) . Find all the tangent lines
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