Contents

8.1 Understanding Functions of Two Variables

Strategy to Investigate Functions of Two Variables: Vary One Variable at a Time

Concentration of a Drug in the Blood

Cobb-Douglas Production Functions

Finding Contours Algebraically

Rate of Change of Airline Revenue

Estimating Partial Derivatives from a Table

Using Partial Derivatives to Estimate Values of the Function

Estimating Partial Derivatives from Contours

Using Units to Interpret Partial Derivatives

8.4 Computing Partial Derivatives Algebraically

Second-Order Partial Derivatives

The Mixed Partial Derivatives Are Equal

8.5 Critical Points and Optimization

Finding Local Maxima/Minima Analytically

How Do We Find Critical Points?

Is a Critical Point a Local Maximum or a Local Minimum?

Graphical Approach: Maximizing Production Subject to a Budget Constraint

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