Chapter 12 Review Important Terms, Symbols, Concepts

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Chapter 12 Review Important Terms, Symbols,
Concepts

• 12.1. First Derivatives and Graphs
• Increasing and decreasing properties of a
  function can be determined by examining a sign
  chart for the derivative.
• A number c is a partition number for f (x) if
  f (c) 0 or f (x) is discontinuous at c. If
  c is also in the domain of f (x), then c is a
  critical value.
• The first derivative test is used to locate
  extrema of a function.

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Chapter 12 Review

• 12.2. Second Derivative and Graphs
• The second derivative of a function can be used
  to determine the concavity of the graph of f.
• Inflection points on a graph are points where the
  concavity changes.
• Concavity of the graph of f (x) can also be
  determined by examining the graph of f (x).
• A graphing strategy is used to organize the
  information obtained from the first and second
  derivatives.

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Chapter 12 Review

• 12.3. LHôpitals Rule
• Limits at infinity and infinite limits involving
  powers of (x-c), ex, and ln x are reviewed. The
  first version of LHôpitals rule applies to
  limits involving the indeterminate form 0/0 as x
  ? c.
• You must always check that LHôpitals rule can
  be applied.
• LHôpitals rule can be applied more than once.
• LHôpitals rule applies to one-sided limits.
• LHôpitals rule applies to limits at infinity.
• LHôpitals rule applies to limits involving the
  indeterminate form ?/?.

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Chapter 12 Review

• 12.4. Curve Sketching Techniques
• The graphing strategy used previously is expanded
  to include horizontal and vertical asymptotes.
• If f (x) n(x)/d(x) is a rational function with
  the degree of n(x) one more than the degree of
  d(x), then the graph of f (x) has an oblique
  asymptote of the form y mx b.

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Chapter 12 Review

• 12.5. Absolute Maxima and Minima
• The steps involved in finding the absolute
  maximum and absolute minimum values of a
  continuous function on a closed interval are
  listed in a procedure.
• The second derivative test for local extrema can
  be used to test critical values, but it does not
  work in all cases.
• If a function is continuous on an interval I and
  has only one critical value in I, the second
  derivative test for absolute extrema can be used
  to find the absolute extremum, but it does not
  work in all cases.

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Chapter 12 Review

• 12.6. Optimization
• The methods used to solve optimization problems
  are summarized and illustrated by examples.