Section 1.6
- State the definition of the natural logarithm and know its domain.
- Correctly use the notation for and properties of the natural
logarithm.
- Solve equations using the natural logarithm and its properties.
- Convert exponential equations between forms that show the percent
rate of change and the continuous rate of change and read such
information from them.
Section 1.7
- State the definition of doubling time and half-life and
understand why they do not depend on initial value or time.
- Find doubling time and half-life and interpret them in applied
problems.
- Construct formulas for compound interest and compute related
quantities.
Section 1.8
- Given formulas for f(x) and g(x), find composite functions
involving f(x) and g(x).
- Given formulas, graphs, or tables for f(x) and g(x), find
specific values of composite functions involving f(x) and g(x).
- Given a composite function, break it apart into an inside
function u and an outer function.
- Apply stretches and shifts to graphs of functions.
Section 1.9
- Identify power functions from formulas and quantities that are
proportional from tables or given information.
- Write formulas relating quantities that are proportional or
inversely proportional and find the constant of proportionality.
- Identify the degree and leading coefficient of polynomial
functions and how they affect the shape of the graph (long term
behavior and numbers of zeros and turning points).
- (p. 95-96) Be able to use the notation of the limit of f(x) as
x-> infinity to describe or compare long term behavior of functions.
Section 2.1
- State the definition of instantaneous rate of change.
- Correctly use the notation for and assign units to the derivative
at a point.
- Find or estimate instantaneous rates of change of functions given
by formulas, tables, and graphs.
- Interpret the instantaneous rate of change at a point as the
slope of the tangent line to the graph at that point.
Section 2.2
- Interpret the derivative as a function and sketch the graph of f
'(x) if given the graph of f(x).
- Find information about f(x) from information about f '(x).
- Find approximate values for f '(x) from a table of values for
f(x).
Section 2.3
- Give units and interpret the meaning of the derivative in
applications.
- Describe what is known about a function from the sign of its
derivative in applications.
- Use the derivative to construct a local linear approximation that
allows you to estimate nearby values of a function.
Section 2.4
- State the definition of and correctly use notation for the second
derivative.
- Determine information about the second derivative from a graph of
the function.
- Determine information about a function from information about its
second derivative.
- Interpret the second derivative in terms of rates of change, including giving units.
Section 2.5
- Estimate marginal cost and marginal revenue from a graph, table,
or values.
- Estimate costs or revenue for nearby quantities using narginal
cost or revenue in a local linear approximation.
- Interpret marginal cost or revenue and related quantities in
applications.
Page 135-140
- Estimate limits by using values closer and closer to the value being approached.
- Decide if a function given by a formula, graph, or words is continuous.
Chapter 3
- Find formulas for derivatives of the given type(s) of functions.
- Use derivative formulas or graphs to compute values of the
derivative at a point.
- Find the equation of the tangent line at a point using a value of
the derivative.
- Use the graph and concavity of the function to compare
approximate values found using the tangent line with the actual value
on the function.
Section
3.1 - powers of x, scalar multiples of functions, sums and
differences of functions, hence any polynomial (including constant and
linear functions)
Section
3.2 - f(x)=a^x, f(x)=ln(x)
Section 3.3 - composite
functions
Section 3.4 - products and
quotients of functions
Section 4.1
- Find and classify all critical values of functions given by
graphs or formulas as a local maximum, local minimum, or neither using
the first or second derivative tests.
- Find information about f(x) from information about zeros and
signs of f '(x).
Section 4.2
- Find inflection points for functions given by graphs or formulas.
- Sketch a possible graph of f(x) given information about f '(x)
and f ''(x).
Section 4.3
- Use the first and second derivatives to determine global extreme
values for a function given by a formula on a closed or open interval.
- Find extreme values and the inputs that produce them in
applications.
- Sketch a possible graph of f(x) given information about its local
and global extreme values.
Section 4.4
- Apply principles from 4.1-4.3 to find maximum revenue and profit,
minimum cost, and production levels where these occur.
Section 4.7
- Know the formula for a logistic function and its properties,
including the meaning of L and the point of diminishing returns.
- Apply principles from calculus and algebra to answer questions
about logistic
models for populations and dose-response curves.
Section 4.8
- Know the formula for drug concentration curves and the effect of
changing parameters a and b in the family ate^(-bt).
- Apply principles from calculus to answer questions about drug
concentration curves.
Section 5.1
- Estimate accumulated change in a function using a table of values
or a graph for the rate of change of that function.
- Determine whether an estimate is an overestimate or an
underestimate based on whether the rate of change is increasing or
decreasing and whether right or left endpoint values are used.
Section 5.2
- Estimate a definite integral of a function using a table of
values or graph of the function.
- Determine the values of n, delta t, and f(t_i) used in estimating
the definite integral of a function.
- Use a calculator to estimate the definite integral of a function
given by a formula.
Section 5.3
- Interpret the definite integral of f(x) in terms of area when
f(x) is positive and when f(x) is both positive and negative on the
interval.
- Estimate a definite integral using a graph of a function that is
both positive and negative.
- Determine the area between two functions (including the case
where one function is 0 or the x=axis) using definite integrals.
Section 5.4
- Estimate the total change in a quantity given information about
its rate of change in a table, graph, or formula.
- Estimate the value of a function if given its initial value and
information about its rate of change.
- Interpret the meaning of the definite integral in applications,
including when the rate of change is positive and negative and when the
function is a drug concentration curve.
Section 5.5
- Interpret the First Fundamental Theorem of Calculus as relating
the definite integral of a rate of change to total change.
- Use the First Fundamental Theorem of Calculus to compute total
cost if given fixed costs and information about the marginal cost.
Second Fundamental Theorem of Calculus
- Interpret an integral with a variable in the upper limit as
describing a function (that we will study again later in Chapter 7 as
an antiderivative).
- Interpret the First and Second Fundamental Theorem of Calculus as
showing that differentiation and integration are opposite processes.
Section 6.1
- Use definite integrals to find the average value of a function on
an interval, including in applications.
- Compare the average value of a function on an interval to the
average of the values of the function at two inputs and describe how
this depends on concavity.
- Interpret the average value of a function on its graph.
Section 7.1
- Find antiderivatives of common functions like x^n with n not -1,
1/x, e^(kx), cos(kx), sin(kx).
- Use the sum, difference, and constant multiple rules to find
antiderivatives.
- Find a particular antiderivative when given further information
about one of its values.
Section 7.2
- Use substitution to find antiderivatives and use correct notation
to describe the substitution.
- Recognize when substitution is needed to find an antiderivative.
Section 7.3
- Compute the exact value of a definite integral or the change in a
function using antiderivatives and the Fundamental Theorem of Calculus.
- Use correct notation when computing definite integrals by
substitution.