Dept. of Mathematics, Texas A&M University
Learning Outcomes
Math 142
A. Identify and articulate your educational goals.
B. Develop an increased understanding of yourself as a student and learner.
C. Functions
1. Recognize the graphs of the identity, square, cube, square root, cube root, and absolute
value functions.
2. Develop and graph piece-wise functions to model real-world situations.
3. Determine a quadratic model for a revenue or profit function and calculate the break-even
point.
4. Distinguish between graphs of exponential functions with different bases and
coefficients.
5. Simplify expressions using properties of exponents.
6. Solve problems involving compound interest. T
7. Solve problems involving continuously compounded interest.
8. Model exponential growth and decay.
9. Determine if a function is one-to-one.
10. Determine the inverse of a one-to-one function.
11. Convert between an exponential and a logarithmic equation.
12. Evaluate simple logarithmic expressions without a calculator.
13. Simplify logarithmic expressions using properties of logarithms.
14. Solve equations involving exponential functions.
15. Solve equations involving logarithmic functions.
D. The Derivative
1. Estimate a limit at a point and a limit at infinity from the graph of a function.
2. Determine the values of x for which a limit does not exist given a graph of a function.
3. Evaluate limits at a point algebraically.
4. Evaluate limits at infinity for rational functions.
5. Identify the intervals on which a function is continuous given its graph or its equation.
6. Locate points of discontinuity for a piece-wise function.
7. Calculate average rate of change.
8. Calculate instantaneous rate of change.
9. Calculate the slope of the secant line to a curve at a point.
10. Write the equation of the tangent line to a curve at a point.
11. Find a formula for the derivative using the limit definition of the derivative.
12. Determine the values of x for which the tangent line is horizontal.
13. Identify the points at which a function is nondifferentiable.
14. Use short-cut rules to find a formula for the derivative of a function.
a. Differentiate power functions.
b. Differentiate the sum or difference of two functions.
c. Differentiate the product or quotient of two functions.
d. Differentiate exponential and logarithmic functions.
e. Differentiate composite functions.
15. Compute marginal cost, marginal revenue, and marginal profit models.
a. Determine the approximate cost, revenue, and profit for the next item.
16. Compute marginal average cost, marginal average revenue, and marginal average profit
models.
17. Determine if demand is elastic, inelastic, or has unit elasticity at a given price level.
Last Saved: 8/26/10 3:21 PM
Dept. of Mathematics, Texas A&M University
E. Graphing and Optimization
1. Analyze the graph of a function.
a. Identify the intervals on which a function is increasing or decreasing.
b. Identify the intervals on which a function is concave up or concave down.
c. Determine the intervals on which the first derivative is positive or negative.
d. Identify the intervals on which the second derivative is positive or negative.
2. Determine local extrema and intervals of increasing and decreasing using the first
derivative.
a. Identify the critical values of a function.
b. Create a sign chart of the characteristics of the first derivative.
3. Match the graph of a function to the graph of its derivative.
4. Calculate higher-order derivatives.
5. Determine the inflection points and concavity of a function.
a. Create a sign chart of the characteristics of the second derivative.
6. Sketch the graph of a function given information about the first and second derivatives.
7. Determine the point of diminishing returns of a total sales model.
8. Sketch the graph of a rational function.
a. Determine the domain, intercepts, and asymptotes of the function.
b. Analyze and unite the properties of the first and second derivatives by using
sign charts.
9. Determine the absolute maximum and minimum values of a function on a given interval.
10. Solve real-world optimization problems.
F. The Integral
1. Evaluate indefinite integrals.
a. Use anti-derivative rules to evaluate an indefinite integral.
b. Use substitution to evaluate an indefinite integral.
2. Find a particular anti-derivative of a derivative satisfying a given condition.
3. Estimate a definite integral by computing Riemann Sums.
4. Calculate a definite integral by using the properties of definite integrals.
5. Evaluate definite integrals by using the Fundamental Theorem of Calculus.
6. Determine the average value of a function on an interval.
7. Calculate the area bounded between two curves. T
8. Calculate the consumers’ and producers’ surplus given supply and demand curves. T
G. Multivariable Calculus
1. Evaluate a function of two or more variables.
2. Plot points in the three-dimensional coordinate system.
3. Sketch a graph of a function in the three-dimensional coordinate system.
4. Evaluate a difference quotient for a function of two variables.
5. Apply business models involving more than one independent variable.
6. Calculate first- and second-order partial derivatives.
7. Determine if a critical point in three dimensions is a local maximum, local minimum, or a
saddle point by using the second derivative test.
8. Apply the method of least-squares to model a data set.
Key: T indicates an outcome heavily dependent on the use of technology.
Last Saved: 8/26/10 3:21 PM