CHS MATH 12 TOPICS FOR EXAM I 2006 - 2007



TOPICS FOR EXAM I

1. Utilize real numbers, inequalities, and lines.

2. Graph functions including polynomial, piecewise, and rational.

3. Find a break-even point, given revenue and cost funtions.

4. Find limits of functions including one-sided limits.

5. Find limits involving infinity. Identify horizontal and vertical asymptotes.

6. Identify conditions required for a function to be classified as continuous.

7. Find points of discontinuity in various functions including piecewise functions and rational functions using the definition of continuity.

8. Determine the profit function, given revenue and cost information.

9. Find rates of change, slopes, and derivatives.

10. Use the definition to find the derivative of a function.

11. Find the derivative using product, quotient, generalized power, and/or chain rule.

12. Write the equation of the tangent line to a curve at a given point.

13. Find and interpret the instantaneous rate of change of a function at a point.

14. Find higher order derivatives.

15. Use derivatives to find marginal, average marginal, velocity and acceleration functions.

16. Find absolute maximum and minimum values of a continuous function on a closed interval.

17. Find relative maximum and minimum points of a function and identify intervals where the function is increasing or decreasing using the first derivative test and the sign diagram.

18. Find points of inflection and intervals of concavity of a function using the second derivative with a sign diagram.

19. Sketch a rational function identifying vertical and horizontal asymptotes, intercepts, domain, and range.

20. Solve optimization word problems.

21. Interpret information from the graph of a function and/or its first derivative and second derivative.

22. Given the graph of a function, sketch its derivative.

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