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1 1 of 6 7/10/2013 8:32 PM 2.2Basic Differentiation Rules and Rates of Change ( ) Question Question Details LarCalc [ ] y = 11 y' = 2. Question Details LarCalc [ ] h() = 8 8 h'() = 3. Question Details LarCalc [ ] f() = 6 f '() = 4. Question Details LarCalc [ ] f(t) = 6t 2 8t 4 f '(t) = 5. Question Details LarCalc [ ] f() = f '() = 6. Question Details LarCalc [ ] y = π cos(θ) sin(θ) 2 y' =

2 2 of 6 7/10/2013 8:32 PM 7. Question Details LarCalc [ ] y = sin() y '() = 8. Question Details LarCalc [ ] 8 y = + 2 cos() (3) 3 y' = 9. Question Details LarCalc [ ] Complete the table. Original Function y = Rewrite y = 8/3 2 Differentiate y' = Simplify y' = 10. Question Details LarCalc MI. [ ] Find the derivative. y = y ' = 11. Question Details LarCalc [ ] Complete the table. Original Function y = π (8) 2 Rewrite Differentiate Simplify

3 3 of 6 7/10/2013 8:32 PM 12. Question Details LarCalc [ ] Complete the table. Original Function 9 Rewrite y = 9 1/2 Differentiate y' = Simplify y' = 13. Question Details LarCalc [ ] Find the derivative. Original Function y = 2 4 Rewrite 2 4 Differentiate Simplify 14. Question Details LarCalc [ ] Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. f (t) = 2 9, ( 3, 2 ) 5t 4 5 f '(3/4) = 16/5 15. Question Details LarCalc [ ] Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. f(θ) = 7 sin(θ) θ, (0, 0) f '(0) = Question Details LarCalc [ ] f() = f '() =

4 4 of 6 7/10/2013 8:32 PM 17. Question Details LarCalc [ ] g(t) = t 2 8 t 3 g'(t) = 18. Question Details LarCalc MI. [ ] f() = f '() = 19. Question Details LarCalc MI.SA. [ ] This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Eercise f() = Question Details LarCalc [ ] f () = f '() = 21. Question Details LarCalc [ ] f '() = 22. Question Details LarCalc [ ] f(t) = 4t 2/3 2t 1/3 + 4 f '(t)=

5 5 of 6 7/10/2013 8:32 PM 23. Question Details LarCalc MI. [ ] f() = cos f '() = 24. Question Details LarCalc MI.SA. [ ] This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Eercise f() = cos 25. Question Details LarCalc MI. [ ] Determine the point at which the graph of the function below has a horizontal tangent line. (If an answer does not eist, enter DNE.) y = (, y) = ( 0, 1 ) 26. Question Details LarCalc MI.SA. [ ] This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Eercise Determine the point at which the graph of the function below has a horizontal tangent line. y =

6 6 of 6 7/10/2013 8:32 PM 27. Question Details LarCalc [ ] Determine the point(s) (if any) at which the graph of the function has a horizontal tangent line. y = cos(), 0 < 2π STEP 1: Find a derivative y'. STEP 2: Set y' = 0 and solve for. 1 = (smaller value) 2 = (larger value) STEP 3: Find the y values by substituting the values from Step 2 into the original function. y 1 corresponds to 1 and y 2 corresponds to 2. List the points where the function has horizontal tangent lines. Submit your answers in terms of pi for π. ( 1, y 1 ) = (, ) ( 2, y 2 ) = (, ) 28. Question Details LarCalc MI. [ ] Find k such that the line is tangent to the graph of the function. Function Line k = 8 f() = k y = Assignment Details Name (AID): 2.2Basic Differentiation Rules and Rates of Change ( ) Submissions Allowed: 5 Category: Homework Code: Locked: Yes Author: Goldsworthy, William ( bgoldsworthy@soroschool.org ) Last Saved: Sep 18, :55 PM EDT Permission: Protected Randomization: Person Which graded: Last Feedback Settings Before due date Question Score Assignment Score Publish Essay Scores Question Part Score Mark Add Practice Button Help/Hints Response Save Work After due date Question Score Assignment Score Publish Essay Scores Key Question Part Score Solution Mark Add Practice Button Help/Hints Response

8/6/2010 Assignment Previewer

8/6/2010 Assignment Previewer Week 5 Tuesday Homework (1322085) Question 123456789101112131415161718 1. Question DetailsSCalcET6 2.8.AE.01. [679727] EXAMPLE 1 The graph of a function f is given to the left. Use it to sketch the graph