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Where " is positive,
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Is concave up
Where " is positive,
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Where has a local minimum,
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Is positive
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Where is concave up,
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Is increasing
Where is concave up,
' ______________________
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Where has a point of inflection,
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Changes signs
Where has a point of inflection,
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Bonus:
Where ' changes from to ,
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Has a local minimumIs concave up
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Where " is negative,
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Is concave down
Where " is negative,
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Where ' is concave down,
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Is decreasing
Where ' is concave down,
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Where ' is increasing,
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Is positive
Where ' is increasing,
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Where ' is positive,
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Is increasing
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Bonus:
Where has a local minimum,
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Bonus:
Changes from – to +Is increasing
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Where has a point of inflection,
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Has a local max / min
Where has a point of inflection,
' ______________________
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Where ' is negative,
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Is decreasing
Where ' is negative,
______________________
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Where " changes signs,
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has a point of inflection
Where " changes signs,
______________________
f
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Where " is positive,
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Is increasing
Where " is positive,
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bonus:
Where ' changes from to ,
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+ −
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bonus:
Has a local maximumIs concave down
Where ' changes from to ,
______________________
f
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+ −
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Where " is negative,
' ______________________
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Is decreasing
Where " is negative,
' ______________________
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Where " is increasing,
' ______________________
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Is concave up
Where " is increasing,
' ______________________
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Where is decreasing,
' ______________________
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Is negative
Where is decreasing,
' ______________________
f
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Where ' is increasing,
______________________
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Is concave up
Where ' is increasing,
______________________
f
f
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Bonus:
Where has a local maximum,
' ______________________
f
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Bonus:
Changes from + to -Is decreasing
Where has a local maximum,
' ______________________
f
f
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Where ' has a point of inflection,
"______________________
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has a local max / min
Where ' has a point of inflection,
"______________________
f
f
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Where ' is concave up,
"______________________
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Is increasing
Where ' is concave up,
"______________________
f
f
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Where ' is decreasing,
______________________
f
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Is concave down
Where ' is decreasing,
______________________
f
f
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Where is increasing,
' ______________________
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Is positive
Where is increasing,
' ______________________
f
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Bonus:
Where " changes from to ,
' ______________________
f
f
+ −
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Bonus:
Has a local maximumIs concave down
Where " changes from to ,
' ______________________
f
f
+ −
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Where ' has local extrema,
______________________
f
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has a point of inflection
Where ' has local extrema,
______________________
f
f
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Where " is decreasing,
' ______________________
f
f
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Is concave down
Where " is decreasing,
' ______________________
f
f
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Where has a local maximum,
"______________________
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Is negative
Where has a local maximum,
"______________________
f
f
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Where is concave down,
' ______________________
f
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Is decreasing
Where is concave down,
' ______________________
f
f
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Bonus:
Where ' has a local maximum,
"______________________
f
f
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Bonus:
Changes from + to -Is decreasing
Where ' has a local maximum,
"______________________
f
f
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Where is concave up,
"______________________
f
f
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Is positive
Where is concave up,
"______________________
f
f
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Where ' is decreasing,
"______________________
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Is negative
Where ' is decreasing,
"______________________
f
f
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Where " has local extrema,
' ______________________
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has a point of inflection
Where " has local extrema,
' ______________________
f
f
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Where is concave down,
"______________________
f
f
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Is negative
Where is concave down,
"______________________
f
f
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Bonus:
Where " changes from to ,
' ______________________
f
f
− +
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Bonus:
Has a local minimumIs concave up
Where " changes from to ,
' ______________________
f
f
− +