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DefinitionsDefinitions 50 40 30 20 10LimitsLimitsOtherOther Misc.Misc. Chapter 2.6 to 2.9 50 40 30 20 10 50 40 30 20 10 50 40 30 20 10 50 40 30 20 10.

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Presentation on theme: "DefinitionsDefinitions 50 40 30 20 10LimitsLimitsOtherOther Misc.Misc. Chapter 2.6 to 2.9 50 40 30 20 10 50 40 30 20 10 50 40 30 20 10 50 40 30 20 10."— Presentation transcript:

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2 DefinitionsDefinitions LimitsLimitsOtherOther Misc.Misc. Chapter 2.6 to Review for the Test Chapter 2.6 to 2.9 Final RoundGraphsGraphs

3 Definitions

4 CheckWork Go Home Go Home 10 Point Question What is the limit definition for the derivative of a function?

5 True or False: If a function is differentiable, then it is continuous. 20 Point Question CheckWork Go Home Go HomeTrue

6 D 30 Point Question Which of the following is not a valid interpretation of f’(t)? A)The instantaneous rate of change of f(t) B) The slope of the tangent to f(t) C) The velocity, if f(t) gives the position as a function of time D) The area under f(t) CheckWork Go Home Go Home

7 Next category please! 40 Point Question Daily Double: the team picking this question gets 80 points! CheckWork Go Home Go Home

8 What is the difference between the two limits? 50 Point Question CheckWork Go Home Go Home f’(a) = slope of a function at a point. f’(x) = a function where the output is the slope of f(x) at any particular point.

9 Limits

10 CheckWork  Go Home Go Home Find the limit: 10 Point Question

11 20 Point Question Find f’(5), if f(x) = 3x+1 CheckWork Go Home Go Home3

12 30 Point Question CheckWork Go Home Go Home Find f’(-1) if f(x) = 2x 2. -4

13 Find the derivative of f(x) = -2x 2 + 3x 40 Point Question f’(x) = -4x +3 CheckWork Go Home Go Home

14 Sketch a graph with the following properties: 50 Point Question CheckWork Go Home Go Home Answers may vary.

15 Graphing

16 If f’(a) is positive, what do we know about f(x) at a? 10 Point Question CheckWork Go Home Go Home f(x) is increasing

17 If f”(x) is negative, what do we know about the graph of f(x)? 20 Point Question CheckWork Go Home Go Home It is concave down.

18 Sketch the graph of f’(x), for graph #1 30 Point Question CheckWork Go Home Go Home

19 40 Point Question Based on the graph, sketch f”(x), for graph #2. CheckWork Go Home Go Home

20 The graph in #3 is the derivative of f(x). Sketch f(x), assuming f(0) = 0 50 Point Question CheckWork Go Home Go Home

21 On the test

22 There will be no derivative if the function is discontinuous, has a sharp corner or has a vertical tangent line at the point. 10 Point Question In general, at what points does a function fail to have a derivative? CheckWork Go Home Go Home

23 Daily Double: The team picking this question gets 40 points! 20 Point Question CheckWork Go Home Go Home

24 No. Limit as x -> 5 is 3/8 (not 0.5) Is this function continuous at x = 5? 30 Point Question CheckWork Go Home Go Home

25 40 Point Question What value must f(D) be to make the graph continuous? Check Work Go Home Go Home3

26 50 Point Question What value for c makes the function continuous at x = 3? CheckWork Go Home Go Home c = 5

27 Miscelaneous

28 May 13th When is Mother’s Day? 10 Point Question CheckWork Go Home Go Home

29 When does registration for Summer and Fall start? 20 Point Question Monday, May 7th CheckWork Go Home Go Home

30 30 Point Question Who founded the Boeing Company? William Boeing CheckWork Go Home Go Home

31 40 Point Question Who is getting leaving “The View”? CheckWork Go Home Go Home Rosie O’Donnel

32 What is the penalty if you don’t make it to the Testing Center before 3 PM on Friday? 50 Point Question CheckWork Go Home Go Home 10% for taking the test late

33 Just kidding. It really is infinity. If Final Question CheckWork Go Home Go HomeThen


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