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Evaluating Functions of Several Variables In Exercises 1–14, find and simplify the function values. See Example 1.
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Chapter 7 Solutions
Calculus: An Applied Approach (MindTap Course List)
- Total Cost The background for this exercise can be found in Exercises 13 and 14 in Section 3.2. The following table gives the total cost C, in dollars, for a widget manufacturer as a function of the number N of widgets produced during a month. Number N Total cost C 200 7900 250 9650 300 11, 400 350 13, 150 a. What are the fixed costs and variable cost for this manufacturer? b. The manufacturer wants to reduce the fixed costs so that the total cost at a monthly production level of 350 will be 12, 975. What will the new fixed costs be? c. Instead of reducing the fixed costs as in part b, the manufacturer wants to reduce the variable cost so that the total cost at a monthly production level of 350 will be 12, 975. What will the new variable cost be?arrow_forwardusing a graphing calculator or computer algebra system. Illustrate local linearity for f (x) = x 2 by zooming in on the graph at x = 0.5arrow_forwardA specific car’s fuel economy in miles per gallon can be approximated by f(x) = 0.00000056x4 – 0.000018x3 +1.38x- 0.38, where x represents the car’s speed in miles per hour. Determine the fuel economy when the car is traveling 40, 50, and 60 miles per hour. Process Questions: What is f(40)?, f(50)?, and f(60)? Which car speed maximizes fuel consumption? Can you suggest some ways or tips on how to save fuel? What do you think is the best way to save fuel? Why? How did the modelling process help you answer the different problems? How do values of one variable behave in terms of the other in the polynomial function that models a real- world situation?arrow_forward
- The table gives the output values that a function assigns to given input values. Input (x) Output (y) −2 −8 4 10 9 25 12 34 Is the function a linear function? Show work to justify your response on paper or in the box below.arrow_forwardWriting a Linear Function In Exercises11–14, (a) write the linear function f that hasthe given function values and (b) sketch thegraph of the function.11. f(1) = 4, f(0) = 6 12. f(−3) = −8, f(1) = 213. f(12) = −53, f(6) = 2 14. f(35) = 12, f(4) = 9arrow_forward
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