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

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Definitions

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

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

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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

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

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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.

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Limits

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

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

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

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

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

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Graphing

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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

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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.

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

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

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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

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On the test

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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

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

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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

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

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

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Miscelaneous

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

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

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

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

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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

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

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