Calculus: Single And Multivariable
7th Edition
ISBN: 9781119444190
Author: Hughes-Hallett, Deborah; Mccallum, William G.; Gleason, Andrew M.; Connally, Eric; Kalaycioglu, Selin; Flath, Daniel E.; Lahme, Brigitte; Lomen, David O.; Lock, Patti Frazer; Lovelock, David; Morris, Jerry; Lozano, Guadalupe I.; Mumford, David; Quinney, D
Publisher: WILEY
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Textbook Question
Chapter 14.4, Problem 1E
In Exercises 1–14, find the gradient of the function. Assume the variables are restricted to a domain on which the function is defined.
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In Exercises 61–64, find an equation for the level surface of the function through the given point.
In Exercises 11–18, find the slope of the function’s graph at the given point. Then find an equation for the line tangent to the graph there.
11. ƒ(x) = x2 + 1, (2, 5) 12. ƒ(x) = x - 2x2, (1, -1)
13. g(x) = x/(x - 2) , (3, 3) 14. 8/ x2 , (2, 2)
15. h(t) = t3, (2, 8) 16. h(t) = t3 + 3t, (1, 4)
17. ƒ(x) = sqrt(x), (4, 2) 18. ƒ(x) = sqrt(x + 1), (8,3).
In Exercises 65–68, find and sketch the domain of ƒ. Then find an equation for the level curve or surface of the function passing through the given point.
Chapter 14 Solutions
Calculus: Single And Multivariable
Ch. 14.1 - Using dierence quotients, estimate fx(3, 2) fy(3,...Ch. 14.1 - Prob. 3ECh. 14.1 - In Exercises 1015, a point A is shown on a contour...Ch. 14.1 - In Exercises 1015, a point A is shown on a contour...Ch. 14.1 - Approximate fx (3, 5) using the contour diagram of...Ch. 14.1 - Figure 14.11 shows the contour diagram of g(x, y)...Ch. 14.1 - Figure 14.13 shows the saddle-shaped surface z =...Ch. 14.2 - Prob. 2ECh. 14.2 - Prob. 5ECh. 14.2 - Prob. 8E
Ch. 14.2 - Prob. 18ECh. 14.2 - Prob. 23ECh. 14.2 - Prob. 27ECh. 14.2 - Prob. 39ECh. 14.2 - Prob. 65ECh. 14.2 - Which of the following functions satisfy the...Ch. 14.3 - In Exercises 18, nd the equation of the tangent...Ch. 14.3 - In Exercises 18, nd the equation of the tangent...Ch. 14.3 - In Exercises 18, nd the equation of the tangent...Ch. 14.3 - In Exercises 18, nd the equation of the tangent...Ch. 14.3 - In Exercises 18, nd the equation of the tangent...Ch. 14.3 - In Exercises 912, nd the dierential of the...Ch. 14.3 - In Exercises 912, nd the dierential of the...Ch. 14.3 - In Exercises 1316, nd the dierential of the...Ch. 14.3 - In Exercises 1316, nd the dierential of the...Ch. 14.3 - In Exercises 1720, assume points P and Q are...Ch. 14.3 - In Exercises 1720, assume points P and Q are...Ch. 14.3 - In Exercises 1720, assume points P and Q are...Ch. 14.3 - Prob. 23ECh. 14.3 - In Exercises 2124, assume points P and Q are...Ch. 14.3 - The tangent plane to z = f(x, y) at the point (1,...Ch. 14.3 - Find an equation for the tangent plane to z = f(x,...Ch. 14.3 - (a). Find the equation of the plane tangent to the...Ch. 14.4 - In Exercises 114, nd the gradient of the function....Ch. 14.4 - In Exercises 114, nd the gradient of the function....Ch. 14.4 - In Exercises 114, nd the gradient of the function....Ch. 14.4 - In Exercises 114, nd the gradient of the function....Ch. 14.4 - In Exercises 1522, nd the gradient at the point....Ch. 14.4 - In Exercises 1522, nd the gradient at the point....Ch. 14.4 - In Exercises 1522, nd the gradient at the point....Ch. 14.4 - In Exercises 2328, which of the following vectors...Ch. 14.4 - In Exercises 2328, which of the following vectors...Ch. 14.4 - Prob. 45ECh. 14.4 - Prob. 48ECh. 14.4 - In Exercises 5051, nd the dierential df from the...Ch. 14.4 - In Exercises 5253, nd grad f from the dierential....Ch. 14.4 - In Problems 5864, nd the quantity. Assume that g...Ch. 14.4 - For f(x,y)=(x+y)/(1+x2) nd the directional...Ch. 14.4 - Let f(x, y) = x2y3. At the point (1, 2), nd a...
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- The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells small radios. Use the information in the figure to solve Exercises 67–72. 35,000 30,000 C(x) = 10,000 + 30x 25,000 20,000 15,000 R(x) = 50x 10,000 5000 100 200 300 400 500 600 700 Radios Produced and Sold 67. How many radios must be produced and sold for the company to break even? 68. More than how many radios must be produced and sold for the company to have a profit? 69. Use the formulas shown in the voice balloons to find R(200) – C(200). Describe what this means for the company. 70. Use the formulas shown in the voice balloons to find R(300) – C(300). Describe what this means for the company. 71. a. Use the formulas shown in the voice balloons to write the company's profit function, P, from producing and selling x radios. b. Find the company's profit if 10,000 radios are produced and sold. 72. a. Use the formulas shown in the voice balloons to write the company's profit function,…arrow_forwardExercises 1-4: A linear function f can be written in the form f(x) = mx + b. Identify m and b for the given f(x). 1. f(x) = 5 – 2x 2. f(x) = 3 – 4x 3. f(x) = -8x 4. f(x) = -6arrow_forwardIn Exercises 49–52, find an equation for and sketch the graph of the level curve of the function ƒ(x, y) that passes through the given point.arrow_forward
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