Learning Outcome 4: Derivatives of Functions of Several Variables

Understand single-valued functions of two or three variables and their derivatives, perform associated computations, and apply understanding and computations to solve problems.

Tablet and Phone users: Tap any box to expand its menu.

Performance Criteria:
  1. Determine average rates of change with respect to position of functions of two and three variables, with the function given as an equation, in table form, or as a contour graph.

  2. Find and interpret (give location, direction, change in dependent variable per unit of change in independent variable) partial derivatives of a function at a point.

  3. Determine whether a function is a solution to a given partial differential equation.

  4. Find vectors and a plane tangent to a surface at a point. Find and use linear approximations of functions of one, two and three variables.

  5. Find and interpret (location, direction, change in dependent variable per unit of change in independent variables) directional derivatives of a function at a point.

  6. Determine the direction in which a function has the greatest rate of increase or decrease at a point, and give that rate. Determine the directions from a point in which a function remains constant.

  7. Find relative minima and maxima of a function of one or two variables. (This includes both the function values {\it and} where they occur.)

  8. Given a contour graph of a function of two variables, determine the locations and approximate values of absolute maxima and minima on a closed region.

  9. Use calculus to find absolute maxima and minima of a function of two variables on a closed region.

  10. Give the appropriate chain rule for a particular situation. Apply a chain rule to find a derivative.

Return to Math 254 page