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Calculus and its applications: 6.1

"Calculus and its applications: 6.1" - Calculus and its applications - Functions of Several variables have objective: find a function value for a function of several variables. | 2012 Pearson Education, Inc. All rights reserved Slide 6.1- Functions of Several Variables OBJECTIVE Find a function value for a function of several variables. 2012 Pearson Education, Inc. All rights reserved Slide 6.1- DEFINITION: A function of two variables assigns to each input pair, (x, y), exactly one output number, f (x, y). 6.1 Functions of Several Variables 2012 Pearson Education, Inc. All rights reserved Slide 6.1- Example 1: For the profit function, find P(25, 10). 6.1 Functions of Several Variables 2012 Pearson Education, Inc. All rights reserved Slide 6.1- 6.1 Functions of Several Variables Quick Check 1 A company’s cost function is given by Find 2012 Pearson Education, Inc. All rights reserved Slide 6.1- Example 2: The total cost to a company, in thousands of dollars, is given by where x dollars is spent for labor, y dollars for raw materials, z dollars for advertising, and w dollars for machinery. Find C(3, 2, 0, 10). 6.1 Functions of Several Variables p. 453, formula 12, there is no “+C” 2012 Pearson Education, Inc. All rights reserved Slide 6.1- Example 3: A business purchases a piece of storage equipment that costs C1 dollars and has capacity V1. Later it wishes to replace the original with a new piece of equipment that costs C2 dollars and has capacity V2. Industrial economists have found that in such cases, the cost of the new piece of equipment can be estimated by the function of three variables 6.1 Functions of Several Variables 2012 Pearson Education, Inc. All rights reserved Slide 6.1- Example 3 (concluded): For $45,000, a beverage company buys a manufacturing tank that has a capacity of 10,000 gallons. Later it decides to buy a tank with double the capacity of the original. Estimate the cost of the new tank. 6.1 Functions of Several Variables 2012 Pearson Education, Inc. All rights reserved Slide 6.1- 6.1 Functions of Several Variables Quick Check 2 a.) Repeat Example 3 assuming that the company buys a . | 2012 Pearson Education, Inc. All rights reserved Slide 6.1- Functions of Several Variables OBJECTIVE Find a function value for a function of several variables. 2012 Pearson Education, Inc. All rights reserved Slide 6.1- DEFINITION: A function of two variables assigns to each input pair, (x, y), exactly one output number, f (x, y). 6.1 Functions of Several Variables 2012 Pearson Education, Inc. All rights reserved Slide 6.1- Example 1: For the profit function, find P(25, 10). 6.1 Functions of Several Variables 2012 Pearson Education, Inc. All rights reserved Slide 6.1- 6.1 Functions of Several Variables Quick Check 1 A company’s cost function is given by Find 2012 Pearson Education, Inc. All rights reserved Slide 6.1- Example 2: The total cost to a company, in thousands of dollars, is given by where x dollars is spent for labor, y dollars for raw materials, z dollars for advertising, and w dollars for machinery. Find C(3, 2, 0, 10). 6.1 Functions of Several .