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 variables to find the approximate partial derivatives.

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

• The slope of a tangent line in the X direction

• The slope of a tangent line in the Y direction

• The change in X values

• The change in contour levels

How do you estimate a partial derivative using a secant line?

• By finding the change in function value and dividing by the change in the respective variable

• By measuring the distance between two points

• By finding the change in contour levels

• By calculating the area under the curve

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

• 270

• 90

• 360

• 135

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

• 10

• 20

• 5

• 15

What is the function value at the point (3, 21) in the first example?

• 360

• 135

• 270

• 90

What is the change in Y used to estimate the partial derivative in the first example?

• 11

• 10

• 12

• 9

In the second example, what is the function value at the point (2, 5)?

• 135

• 90

• 180

• 270

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

• 10

• 15

• 22.5

• 30

What is the function value at the point (4, 5) in the second example?

• 270

• 180

• 90

• 135

What is the change in X used to estimate the partial derivative in the second example?

• 4

• 1

• 2

• 3