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