Math 71 Supplement 10-6-09

Math 71 Supplement 10-6-09 - y = 2 x parallel to 2 x- 3 y =...

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Math 71 Supplement 10-6-09 Find the derivatives of the following functions: 1. f x ( ) = 2 e x - 5 x 2 + p 2. f x ( ) = 2 e x +2 - 3 x 2 + 4 3. f x ( ) = 2 e 2 x - 5ln x 2 + p 4. f x ( ) = 2ln e x - 5 x 2 + x - 9 5. f x ( ) = 2 e ln x + 7 x 4 6. f x ( ) = 2ln x + e x 7. f x ( ) = e x ln x Find the equation of the tangent line to the graph of f at the indicated value of x . 8. f x ( ) = 2 e x , x = 0 9. f x ( ) = 2 e x , x =1 10. f x ( ) = 2 e x , x = - 1 11. f x ( ) = 4ln x 3 , x =1 12. f x ( ) = 4ln x 3 , x = e 13. f x ( ) = 4ln x 3 , x = e 3 Note that a b = e b ln a . Use this to differentiate the following functions: 14. f x ( ) = 2 x 15. f x ( ) = 5 x 16. f x ( ) = 3 x - x 3 17. f x ( ) = e x + x e 18. At which points is the tangent line to y = 2 e - x 2 horizontal? 19. At which points does the tangent line to y = ln x pass through the origin? 20. At which points is the tangent line to
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Unformatted text preview: y = 2 x parallel to 2 x- 3 y = 22 ? Answers: 1. f ' x ( ) = 2 e x- 10 x 2. f ' x ( ) = 2 e 2 e x- 3 2 x 2- 1 3. f ' x ( ) = 4 e 2 x-10 x 4. f ' x ( ) = 3- 10 x 5. f ' x ( ) = 2 + 28 x 3 6. f ' x ( ) = 2 x + e x 7. f x ( ) = e x 1 x + ln x 8. y = 2 x + 2 9. y = 2 ex 10. y = 2 x e + 4 e 11. y =12 x- 1 ( ) 12. y = 12 x e 13. y = 12 x e 3 + 24 14. f ' x ( ) = 2 x ln2 15. f ' x ( ) = 5 x ln5 16. f ' x ( ) = 3 x ln3- 3 x 2 17. f ' x ( ) = e x + ex e- 1 18. (0,2) 19. ( e ,1) 20. 1 ln2 ln3- ln 2ln2 ( ) ( ) , 3 2ln2 2 1 ln 2...
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