MATH 131-505 Spring 2015
Review III
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Wen
Liu
4.2
• Defintion of absolute maximum/absolute minimum, local maximum/local minimum, and critical number.
• Be able to use the Closed Interval Method to do problems like 6 or 7 on page 3.
4.3
• Know the Increasing/Decreasing Test, The First Derivative Test, Concavity Test, and the
Second Derivative Test.
• Given f (x), be able to find local maximum/local minimum, inflection points, intervals where
f is increasing/decreasing and concave up/concave down.
4.6: Know how to step up and solve optimization problems similar to those appeared in HW or notes.
4.8
• Know the table on page 1.
• Know how to find the most general solutions f to f 0 . Be able to cover f using initial conditions,
i.e. problem 5 on page 3.
5.1: be able to draw the rectangles and use left/right/middle point rules to approximate an integral.
5.2
• Know how to find an integral by areas, i.e. example 3 on page 2.
• Know the properties of the definite integral.
5.3: Know the table of indefinite integrals and use it to compute definite/indefinite integrals.
5.4
• Know the Fundamental Theorem of Calculus and use it to compute the derivative of an integral.
• Be able to do problems similar to examples 1, 2 on page 1,2
5.5: be able to use the substitution rule to evaluate definite/indefinite integrals.
Review quizzes/notes
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