Brief Calculus Unit III Assignment

Brief Calculus Unit III Assignment - ( ) (--+-= x x x x x f...

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Brief Calculus Assignment: Directions: Find the derivative of the given function using the derivative rules learned so far. Show all work and steps on a separate piece of paper. (#1 – 12) 1. f x x x x ( ) = - + - 7 8 5 3 2 3 2. 3 1 ) ( x x f = 3. x x x x f 7 ) ( 2 + = 4. ( 29 π x e x f x + = 2 5. 5 7 ) ( 3 + = x x x f 6. 5 5 ) ( 2 2 + - = x x x f 7. x e x x f 20 6 8 ) ( = 8. x x x f 2 4 5 6 ) ( + = 9. f(x) = 3 2 3 5 x x - 10. 2 4 8 ) ( x x e x f - = 11. f(x) = ln(x 2 + 7x + 12) 6 12. ( 29 - + = 1 1 2 3 ln ) ( 4 2 x x x x f 13. Find an equation of the tangent line to f(x) = 2x 5 + 2x when x = -1.
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14. Given s(t) = -4t 2 + 6t + 5, where s is measured in feet and t in seconds, find the following: a) Find the velocity function, then evaluate when t = 1 second b) Find the acceleration function, then evaluate when t = 2 seconds c) How long does it take for the object to hit the ground? 15. Find the average rate of change for 1 3 2 ) ( 2 + + = x x x f on [ -1, 8 ]. Directions: Find the derivative of the given function using the derivative rules learned so far. Show all work and steps on a separate piece of paper. (#16 – 23) 16. Differentiate ( 29 9 5 4 3 ) 5 ( 8 ) 5 ( ) 6
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Unformatted text preview: ( ) (--+-= x x x x x f 17. f(x) = ( 29 7 3 4 x x + 18. f(x) = ( 29 ( 29 2 4 7 3 2 + +-x x x 19. g(x) = ( 29 ( 29 12 2 10 1 5 2 3 +--x x x 20. g(t) = ( 29 ( 29 4 3 3 2 7 5 6-+ t t 21. h(x) = 3 ) 5 2 ( 1 3-+ x x 22. g(w) = 1 2 2 2 + + w w w 23. f(x) = x 2 e x Directions: Use the given demand function to find the rate of change (with proper units) in the demand x of an item sold for the given price p in dollars. 24. x(p) = +-1 5 3 1 275 p p , p = $4 25. The model f(t) = 1 1 2 2 + +-t t t measures the percent of the normal level of oxygen in a pond, where t is the time in weeks after organic waste is dumped into a pond, t > 0 weeks. Directions: Find the rates of change (with proper units) of f with respect to t when a) t = 0.5 b) t = 2 c) t = 8 26. What does each of the answers in # 25 represent?...
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Brief Calculus Unit III Assignment - ( ) (--+-= x x x x x f...

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