Study Guide 6  (For week of 10/3/00-10/12/00)
(Math 2422, Calculus III, Section 002, Fall 2000)

REMINDER: Final Exam will be Thursday 10/12/00 in class. The test will cover up through Section 12.6

Homework:  Read Sections 12.5-12.6 and work the following problems. You do not need to turn any of these in, and there will not be a quiz on this material. However, this material will appear on the final exam.

  • Section 12.5: 1, 7, 15, 21, 26, 42
  • Section 12.6: 7, 9, 15, 27, 32, 45, 51, 54

    Key Skills :

    1. Use the chain rule to calculate the derivatives of functions with respect to a single independent variable. (12.5: 1, 7)
    2. Use the chain rule to calculate the partial derivatives of functions with respect to several independent variables. (12.5: 15)
    3. Calculate a derivative or partial derivative using implicit differentiation. (12.5: 21, 26)
    4. Calculate the directional derivative of a function in a given direction. (12.6: 7,9,15)
    5. Find the gradient of a function or several variables. (12.6: 27,32)
    6. Use the gradient to find a directional derivative. (try this on 12.6: 7,9,15)
    7. Find the maximum value (over all possible directions) of the directional derivative of a function at a given point. (12.6: 27, 32)
    8. Find the direction of maximum or minimum increase of a function. (12.6: 54)
    9. Use the gradient to find a direction normal to the level curves of a function. (12.6: 45, 51)