Sign charts can provide a useful tool to investigate and

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New Policy on Use of Sign Charts to Justify
Local Extrema
Sign charts can provide a useful tool to
investigate and summarize the behavior of a
function. We commend their use as an
investigative tool. However, the Development
Committee has recommended and the Chief Reader
concurs that sign charts, by themselves, should
not be accepted as a sufficient response when a
problem asks for a justification for the
existence of either a local or an absolute
extremum at a particular point in the domain.
This is a policy that will take effect with the
2005 AP Calculus exams and Reading.
AP Calculus AB Home Page, Exam Information On
the role of sign charts
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AB 5 (2004)
(c) Find all values of x in the open interval
(5,4) at which g attains a relative maximum.
Justify your answer. (d) Find the absolute
minimum value of g on the closed interval 5,4.
Justify your answer.
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AB 5 (2004)
(c) Find all values of x in the open interval
(5,4) at which g attains a relative maximum.
Justify your answer.
Max at x 3
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AB 5 (2004)
(c) Find all values of x in the open interval
(5,4) at which g attains a relative maximum.
Justify your answer.
Max at x 3 because g' changes from positive to
negative at x 3
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AB 5 (2004)
(d) Find the absolute minimum value of g on the
closed interval 5,4. Justify your answer.
Absolute min is g( 4) 1
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AB 5 (2004)
(d) Find the absolute minimum value of g on the
closed interval 5,4. Justify your answer.
Absolute min is g( 4) 1 because g' changes
from negative to positive at x 4, g' is
negative on (5,4) (so g(5) gt g( 4) ), and
g(4) g(2) gt g( 4) because g' gt 0 on (
4,1)?(1,2).
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The Changing Face of Calculus First-Semester
Calculus as a High School Course Featured
article on the home page of the MAA www.maa.org