Calculus Objectives and Assignments

Ch. 4 – Applications of Derivatives

Objectives

Students will be able to:

  1. Know and understand the definition of (Global) Extreme Values, Local (Relative) Extreme Values, and apply the process for finding these values in a variety of functions.
  2. Know and apply the Extreme Value Theorem (EVT).
  3. Identify critical points of a function.
  4. Know and apply the Mean Value Theorem (MVT) for derivatives to functions.
  5. Identify intervals that a function is increasing or decreasing based on the derivative.
  6. Know and understand the definition of the antiderivative of a function.
  7. Know and apply the First Derivative Test for Local Extrema.
  8. Know and apply the definition of Concavity using the first derivative as well as the Concavity Test using the second derivative.
  9. Know and understand the definition of a Point of Inflection.
  10. Know and apply the Second Derivative Test for Local Extrema.
  11. Connect the graphs of f’ and f” to the graph of f and be able to sketch the other two given one of the three.
  12. Understand and apply differentiation to modeling functions that require optimization of a situation in business, industry, economics, or mathematics.

(Second Semester Topics from Chapter 4 – Objectives #13-16)

  1. Calculate a linear approximation (linearization) of a function using the definition.
  2. Know and apply Newton’s Method for approximating a zero of a function.
  3. Understand and apply differentials to functions, when appropriate.
  4. Know and apply solution strategies for solving related rate equations and problem solving situations.

Assignments

1/3p. 184 #2-18 even

1/4p. 184-5 #20-30 even, 39-42, 45-50

1/5Worksheet

1/6p. 192 #2-14 even, 15-18

1/9p. 192 #21-29, 40, 42

1/10Finish p. 192 assignments

1/11p. 203-4 #2-24 even

1/12p. 204-5 #26-42 even, 47, 48

1/13Finish p. 204 assignments

1/17Review for Quiz

1/18Review for Quiz

1/19Quiz Ch. 4 Sec. 1-4

1/20Review for Final Exams

1/23Review for Final Exams

1/24Review for Final Exams

1/25-27Final Exams

12/15p. 229 #2-22 even

12/16p. 230 #24-30 even, 31-36, 39-42

12/17p. 237-8 #2-10 even, 11-13, 16-20 even

12/18p. 239-40 #21, 22, 24-34 even

12/19Finish Related Rates assignments

Work on Review Problems over Winter Break:

p. 242 #2-26 even

p. 242-3 #28-36 even, 37-40, 43, 45

p. 244-5 #46-50 even, 51, 52-62 even

1/5-6Review for Test

1/7-8Review for Test and Final Exams

1/9Ch. 4 Test