Guidelines in reviewing for Exam 2
Exam 2 is cumulative, but will focus upon class material in
Sections 3.5-3.9 and 4.1-4.3.
Following is a list amassing together the daily goals for days
covering material in the sections listed above. In studying for
this exam, you are of course encouraged to look over class notes
and examples, homework (don't just look over your past write-ups;
try to re-work a smattering of assigned problems “from
scratch”) and problems from the “Practice Exercises”
sections at the ends of chapters. You should also assess your
readiness for the exam based on the list of goals.
Goals for Class Date: Oct. 1, 2007
Students should be able to
- Write the statement of the chain rule.
- Identify, in a top-down fashion, the various
derivative rules (including the chain rule)
whose use is required in order to find the
derivative of a given function.
- Employ the chain rule in finding derivatives
of composite functions.
Goals for Class Date: Oct. 2, 2007
Students should be able to
- graph curves given parametrically.
- go back and forth between expressions in the form
y = f(x) and parametric form
x = x(t), y = y(t).
- Write equations for line segments and other rudimentary
curves in parametric form.
Goals for Class Date: Oct. 3, 2007
Students should be able to
- understand the assumptions behind implicit differentiation.
- see the connection between the implicit differentiation
and the chain rule.
- use implicit differentiation to find dy/dx
along various curves.
Goals for Class Date: Oct. 4, 2007
Students should be able to
- determine if a function has an inverse.
- sketch the graph of the inverse function knowing
the graph of the function.
- find derivatives for various inverse functions.
- find derivatives for various expressions involving
exponential functions ax and the
natural log function.
Goals for Class Date: Oct. 5, 2007
Students should be able to
- continue finding derivatives of inverse functions,
particularly the arc-trigonometric ones.
- find derivatives of expressions involving the
arc-trigonometric functions.
- use logarithmic differentiation, particularly for
finding derivatives of expressions of the form
(varying quantity)(varying exponent).
Goals for Class Date: Oct. 8, 2007
Students should be able to
- Write relevant equations depicting a verbal scenario.
- Use implicit differentiation on an equation to find
relationships between rates of change for the various
variables.
- Use the above to answer related rate questions.
Goals for Class Date: Oct. 12, 2007
Students should be able to
- state sufficient conditions under which a function
has an absolute maximum and minumum.
- state what the term critical point of f
means in general, and find any/all such points for
various f.
- state what is meant by the terms absolute maximum
and absolute minumum, and use calculus to find
absolute extrema for various f.
Goals for Class Date: October 16, 2007
Students should be able to
- give a complete statement of the Mean Value Theorem,
along with the special case known as Rolle's Theorem.
- understand what the Mean Value Theorem is saying,
both graphically, and in terms of average vs. instantaneous
rates of change.
- identify situations in which the hypotheses of the
Mean Value Theorem are in place, and use it to answer
questions in those situations.
Goals for Class Date: October 17, 2007
Students should be able to
- understand the relationship between the sign of a function's
derivative and its increasing/decreasing behavior, as expressed
in Corollary 3, p. 254.
- apply the first derivative test (found in the box on p. 256)
to find local extrema.
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