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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 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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