Estimating Partial Derivatives

The video tutorial explains how to estimate the value of partial derivatives using contour maps. It provides two examples: one for estimating the partial derivative with respect to Y and another for X. The process involves using the slope of a secant line to approximate the slope of a tangent line at a given point. The tutorial demonstrates how to select points on the contour map and calculate the changes in function values and coordinates to find the approximate partial derivatives.

What does the partial derivative of a function with respect to Y represent in a contour map?

• The slope of the tangent line in the X direction

• The slope of the tangent line in the Y direction

• The change in the function value with respect to Z

• The change in the function value with respect to X

How do you estimate the partial derivative of a function with respect to Y using a contour map?

• By finding the slope of a tangent line in the X direction

• By using the average of function values

• By finding the slope of a secant line in the Y direction

• By calculating the change in X over the change in Y

In the example given, what is the function value at the point (3, 30)?

• 360

• 90

• 270

• 135

What is the estimated partial derivative of F with respect to Y at the point (3, 30)?

• 20

• 15

• 5

• 10

What is the first step in estimating the partial derivative of F with respect to X?

• Sketch a vertical line parallel to the Y-axis

• Sketch a horizontal line parallel to the X-axis

• Calculate the average function value

• Find the midpoint of the contour map

What is the function value at the point (2, 5) in the second example?

• 135

• 90

• 180

• 270

In the second example, what is the estimated function value at the point (4, 5)?

• 90

• 135

• 180

• 225

What is the estimated partial derivative of F with respect to X at the point (2, 5)?

• 30

• 22.5

• 15

• 10

Which line is used to approximate the partial derivative of F with respect to X?

• A secant line in the X direction

• A tangent line in the Z direction

• A secant line in the Y direction

• A tangent line in the Y direction

What is the change in the function value used to estimate the partial derivative of F with respect to X in the second example?

• 90

• 45

• 135

• 180