Applied Calculus Course Objectives

1.1.1    Define:  function, domain, range, independent variable, dependent variable.

1.1.2    Given a rule for a function, represent that function with a table and a graph.  (Exercise Set 1.1: 59-72)

1.1.3    Given a rule, table, or graph for a relation, determine whether or not the relation is a function.  If the relaton
            is a function, specify its domain and range.  (Exercise Set 1.1:  1-6, 25-30, 43-50)

1.1.4    Define:  increasing function, decreasing function

1.1.5    Given the graph of a function, describe were the function is increasing/decreasing and discuss the concavity
            of the function.  (Exercise Set 1.1:  31)

1.1.6    Given the graph of a function, answer selected questions about the function.  (Exercise Set 1.1: 7, 39, 40, 41)

1.1.7    Demonstrate knowledge of functional notion.  (Exercise Set 1.1:  32-38)

1.2.1    Given a description of a situation that can be appropriately represented by a linear model, formulate a
            linear model for the situation, interpret the meaning of the slope and intercept of the graph of your model
            and use your model to address questions about the situation.  (Exercise Set 1.2:  15-25)

1.2.2    Given a linear model(s) for a situation, employ the model(s) to address selected questions about the situation.
            (Exercises Set 1.2:  26, 31, 32)

1.2.3    Given a linear function with a specified interval domain, find the maximum and minimum values of the
             function and specify where those extreme values occur.  (See class notes.)

1.4.1    Define:  quadratic function

1.4.2    Given a rule for a quadratic function, produce its graph and discuss properties of the function/graph.
            (Exercise Set 1.4: 1-8, 13-24)

1.4.3    Given a quadratic revenue function and a linear cost function, specify the profit function, find the maximum
            value of the profit function, and find the break-even quantities (if they exist).  (Exercise Set 1.4:  31-34)

1.4.4    Given a quadratic profit function, find the break-even quantities and the maximum profit.
            (Exercise Set 1.4:  35-38)

1.4.5    Given a description of a situation that can be appropriately represented by a quadratic model, formulate
            a quadratic model for the situation, graph your model and use your model to address questions about the
            situation.  (Exercise Set 1.4:  46-57)

1.4.6    Given a quadratic function with a specified interval domain, find the maximum and minimum values of the
             function and specify where those extreme values occur.  (See class notes.)

1.5.1    Sketch the graphs of selected exponential functions.  (Exercise Set 1.5:  1-7)

1.5.2    Determine how much is in an account based on a specified annual rate r, a specified compounding period n,
            an initial principal P, and a specified time period t (in years).  (Exercise Set 1.5: 39, 40)

1.5.3    Find the present value of a specified amount F with a specified annual rate of return r, the number of years t,
            and an indicated compounding.  (Exercise Set 1.5:  45, 46)

1.5.4    Apply the concepts of exponential growth and compounding in solving applied problems.
            (Exercise Set 1.5: 53, 55)

1.6.1    Apply basic graphing principles such as vertical shift, horizontal shift, reflection, expansion, and contraction
            in graphing functions.  (Exercise Set 1.6.1:  11-11-37 odd)

1.6.2    Apply special functions and graphing techniques in solving applied problems.  (Exercise Set 1.6:  55, 57, 59)

1.7.1    Given two functions with specified domains determine the sum, difference, product, quotient, and composition
            of those functions and specify their respective domains.  (Exercise Set 1.7:  1-9 odd, 15-23 odd)

1.8.1    Use a logarithm function in solving problems.  (Exercise Set 1.8:  48-51)

2.1.1    Evaluate limits.  (Exercise Set 2.1:  26-31)

2.2.1    Given the graph of a function, specify where the function is (is not) continuous.  (Exercise Set 2.2: 1, 2)

2.2.2    Evaluate limits at infinity:  (Exercise Set 2.2:  19-30)

2.2.3    Employ the concepts of continuity and limit at infinity in solving problems.  (Exercise Set 2.2:  44, 45, 47, 49)

2.3.1    Compare the concepts "average rate of change" and "instantaneous rate of change."

2.3.2    Given a function describing the position of an object as a function of time, find the instantaneous velocity
            of the object at specified times.  (Exercise Set 2.3:  1-8 all)

2.3.3.    Find the instantaneous rate of change of functions at specified points.  (Exercise Set 2.3:  11-21 odd)

2.3.4    Given the graph of a function identify where the rate of change is positive/negative/zero.
            (Exercise Set 2.3:  23, 25)

2.3.5    Given the equation for a curve, find the equation of the line tangent to the curve at a specified point.
            (Exercise Set 2.3:  29, 30)

2.3.6    Employ the concepts of average and  instantaneous rate of change in solving problems.
            (Exercise Set 2.3:  55-67 odd)

2.4.1    State the definition of the derivative exactly as in the shaded box at the top of page 157 in the text.

2.4.2    Show how to use the definition of the derivative to find the derivative of a quadratic function.
            (Exercise Set 2.4:  3, 5)

2.4.3    Given a rule for a function, specify a rule for the derivative of the function.  (Exercise Set 2.4:  1-6)

2.4.4    Given the graph of a function, identify where the function's derivative exists (does not exist).
            (Exercise Set 2.4:  27, 28)

2.4.5    Given graphs of functions and graphs of derivatives of functions, match the graph of each function and
            the graph of its derivative.  (Exercise Set 2.4:  31-36)

2.5.6    Apply the derivative concept in solving problems.  (Exercise Set 2.4:  47, 48, 49)

2.*       Work problems like the following ones in the Review Exercises on pp. 168 170:
            1-11 all, 32, 44, 45, 53, 54, 55

3.1.1     By inspection, specify derivatives of polynomial, power, and exponential functions.
            (Exercise Set 3.1:  1-33 odd)

3.1.2     Show how to employ the concept of the derivative in solving applied problems.
             (Exercise Set 3.1:  73-85)

3.2.1     Given a function that is the product or quotient of polynomial, power, or exponential functions,
             apply the product or quotient rule to specify the derivative of the given function.
             (Exercise Set 3.2:  1-21 odd)

3.2.2     Employ the product or quotient rule for differentiation in solving applied problems.
             (Exercise Set 3.2:  33, 35)

3.4.1     Employ the chain rule in finding the derivatives of specified functions.  (Exercise Set 3.3:   1-9 odd)

3.5.1     Employ the derivative and the concepts of marginal cost, marginal revenue, and marginal profit in
             solving problems.  (Exercise Set 3.5:  1-9 odd)

4.1.1     Employ the First Derivative Test to find the relative extrema of a function.
             (Exercise Set 4.1:  13, 15, 21, 23)

4.1.2     Employ the First Derivative Test in solving applied optimization problems.
             (Exercise Set 4.1:  51-57 odd,  63, 65, 71)

4.3.1     Show how to employ concepts of calculus to find the absolute extrema of specified functions.
             (Exercise Set 4.3:  11-17 odd, 23)

4.3.2     Show how to apply concepts of calculus in solving applied extreme value problems.
             (Exercise Set 4.3:  43-55 odd)

5.1.1    Given one value of a polynomial or exponential function and its derivative, specify a rule for
            the function.  (Exercise Set 5.1:  41-51 odd)

5.1.2    Specify a family of functions that all have the same specified derivative.  That is, find the
            antiderivative of a specified function.  (Exercise Set 5.1:  1-23 odd)

5.3.1    Given a velocity function over a specified time interval, find the distance traveled over that
            time interval.  (Exercise Set 5.3:  11-17 odd using method developed in class.)

5.5.1    Evaluate some definite integrals.  (Exercose Set 5.5:  1-13 odd)

5.5.2    Solve some applied problems using integration.  (Exercise Set 5.5: 41-47 odd)

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