EBK APPLIED CALCULUS, ENHANCED ETEXT
6th Edition
ISBN: 9781119399353
Author: DA
Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT
expand_more
expand_more
format_list_bulleted
Question
Chapter 8.4, Problem 16P
To determine
To find all the points where partial derivative of below function are both zero.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Both first partial derivatives of the function f(x,y) are zero at the given points. Use the second-derivative test to determine the nature of f(x,y) at each of these points. If the second-derivative test
is inconclusive, so state.
f(x,y) = 6x² - 12xy + 2y³ - 18y; (-1,-1), (3,3)
What is the nature of the function at (-1,-1)?
O A. f(x,y) has neither a relative maximum nor a relative minimum at (-1,-1).
B. f(x,y) has a relative minimum at (-1,-1).
O C. f(x,y) has a relative maximum at (-1,-1).
D. The second-derivative test is inconclusive at (-1,-1).
What is the nature of the function at (3,3)?
A. f(x,y) has neither a relative maximum nor a relative minimum at (3,3).
OB. f(x,y) has a relative minimum at (3,3).
C. f(x,y) has a relative maximum at (3,3).
D. The second-derivative test is inconclusive at (3,3).
D
The cost (in dollars) of manufacturing one item is given by
C(x, y) = 70 + 4x + 9y
where x is the cost of 1 hour of labor and y is the cost of 1 pound of material.
(a) If the hourly cost of labor is $25, and the material costs $6 per pound, what is the cost of manufacturing one of these items?
2$
(b) Find the partial derivative of C with respect to x.
Cx =
Both first partial derivatives of the function f(x.y) are zero at the given points. Use the second-derivative test to determine the nature of f(x.y)
each of these points. If the second-derivative test is inconclusive, so state.
f(xy) %3D 12x2 - 24ху + 2у3-72y: (-2, -2), (6,6)
Compute D(x.y) =
дх ду
D(x.y) =
What is the nature of the function at (-2, -2)?
O A. f(x.y) has a relative maximum at (- 2,- 2).
O B. f(x.y) has a relative minimum at (- 2, - 2).
O C. f(x.y) has neither arelative maximum nor a relative minimum at (- 2,-2).
O D. The second-derivative test
inconclusive at (-2,-2).
What is the nature of the function at (6,6)?
O A. f(x.y) has a relative minimum at (6,6).
O B. f(x,y) has a relative maximum at (6,6).
O C. f(x.y) has neither a relative maximum nor a relative minimum at (6,6)
O D. The second-derivative test is inconclusive at (6,6).
Chapter 8 Solutions
EBK APPLIED CALCULUS, ENHANCED ETEXT
Ch. 8.1 - Prob. 1PCh. 8.1 - Prob. 2PCh. 8.1 - Prob. 3PCh. 8.1 - Prob. 4PCh. 8.1 - Prob. 5PCh. 8.1 - Prob. 6PCh. 8.1 - Prob. 7PCh. 8.1 - Prob. 8PCh. 8.1 - Prob. 9PCh. 8.1 - Prob. 10P
Ch. 8.1 - Prob. 11PCh. 8.1 - Prob. 12PCh. 8.1 - Prob. 13PCh. 8.1 - Prob. 14PCh. 8.1 - Prob. 15PCh. 8.1 - Prob. 16PCh. 8.1 - Prob. 17PCh. 8.1 - Prob. 18PCh. 8.1 - Prob. 19PCh. 8.1 - Prob. 20PCh. 8.1 - Prob. 21PCh. 8.1 - Prob. 22PCh. 8.1 - Prob. 23PCh. 8.1 - Prob. 24PCh. 8.1 - Prob. 25PCh. 8.1 - Prob. 26PCh. 8.1 - Prob. 27PCh. 8.1 - Prob. 28PCh. 8.1 - Prob. 29PCh. 8.1 - Prob. 30PCh. 8.2 - Prob. 1PCh. 8.2 - Prob. 2PCh. 8.2 - Prob. 3PCh. 8.2 - Prob. 4PCh. 8.2 - Prob. 5PCh. 8.2 - Prob. 6PCh. 8.2 - Prob. 7PCh. 8.2 - Prob. 8PCh. 8.2 - Prob. 9PCh. 8.2 - Prob. 10PCh. 8.2 - Prob. 11PCh. 8.2 - Prob. 12PCh. 8.2 - Prob. 13PCh. 8.2 - Prob. 14PCh. 8.2 - Prob. 15PCh. 8.2 - Prob. 16PCh. 8.2 - Prob. 17PCh. 8.2 - Prob. 18PCh. 8.2 - Prob. 19PCh. 8.2 - Prob. 20PCh. 8.2 - Prob. 21PCh. 8.2 - Prob. 22PCh. 8.2 - Prob. 23PCh. 8.2 - Prob. 24PCh. 8.2 - Prob. 25PCh. 8.2 - Prob. 26PCh. 8.2 - Prob. 27PCh. 8.2 - Prob. 28PCh. 8.2 - Prob. 29PCh. 8.2 - Prob. 30PCh. 8.2 - Prob. 31PCh. 8.2 - Prob. 32PCh. 8.2 - Prob. 33PCh. 8.2 - Prob. 34PCh. 8.2 - Prob. 35PCh. 8.2 - Prob. 36PCh. 8.2 - Prob. 37PCh. 8.2 - Prob. 38PCh. 8.2 - Prob. 39PCh. 8.2 - Prob. 40PCh. 8.2 - Prob. 41PCh. 8.2 - Prob. 42PCh. 8.2 - Prob. 43PCh. 8.2 - Prob. 44PCh. 8.3 - Prob. 1PCh. 8.3 - Prob. 2PCh. 8.3 - Prob. 3PCh. 8.3 - Prob. 4PCh. 8.3 - Prob. 5PCh. 8.3 - Prob. 6PCh. 8.3 - Prob. 7PCh. 8.3 - Prob. 8PCh. 8.3 - Prob. 9PCh. 8.3 - Prob. 10PCh. 8.3 - Prob. 11PCh. 8.3 - Prob. 12PCh. 8.3 - Prob. 13PCh. 8.3 - Prob. 14PCh. 8.3 - Prob. 15PCh. 8.3 - Prob. 16PCh. 8.3 - Prob. 17PCh. 8.3 - Prob. 18PCh. 8.3 - Prob. 19PCh. 8.3 - Prob. 20PCh. 8.3 - Prob. 21PCh. 8.3 - Prob. 22PCh. 8.3 - Prob. 23PCh. 8.3 - Prob. 24PCh. 8.3 - Prob. 25PCh. 8.3 - Prob. 26PCh. 8.3 - Prob. 27PCh. 8.3 - Prob. 28PCh. 8.3 - Prob. 29PCh. 8.3 - Prob. 30PCh. 8.3 - Prob. 31PCh. 8.3 - Prob. 32PCh. 8.3 - Prob. 33PCh. 8.3 - Prob. 34PCh. 8.3 - Prob. 35PCh. 8.3 - Prob. 36PCh. 8.3 - Prob. 37PCh. 8.3 - Prob. 38PCh. 8.3 - Prob. 39PCh. 8.3 - Prob. 40PCh. 8.4 - Prob. 1PCh. 8.4 - Prob. 2PCh. 8.4 - Prob. 3PCh. 8.4 - Prob. 4PCh. 8.4 - Prob. 5PCh. 8.4 - Prob. 6PCh. 8.4 - Prob. 7PCh. 8.4 - Prob. 8PCh. 8.4 - Prob. 9PCh. 8.4 - Prob. 10PCh. 8.4 - Prob. 11PCh. 8.4 - Prob. 12PCh. 8.4 - Prob. 13PCh. 8.4 - Prob. 14PCh. 8.4 - Prob. 15PCh. 8.4 - Prob. 16PCh. 8.4 - Prob. 17PCh. 8.4 - Prob. 18PCh. 8.4 - Prob. 19PCh. 8.4 - Prob. 20PCh. 8.4 - Prob. 21PCh. 8.4 - Prob. 22PCh. 8.4 - Prob. 23PCh. 8.4 - Prob. 24PCh. 8.4 - Prob. 25PCh. 8.4 - Prob. 26PCh. 8.4 - Prob. 27PCh. 8.4 - Prob. 28PCh. 8.4 - Prob. 29PCh. 8.4 - Prob. 30PCh. 8.4 - Prob. 31PCh. 8.4 - Prob. 32PCh. 8.4 - Prob. 33PCh. 8.4 - Prob. 34PCh. 8.4 - Prob. 35PCh. 8.4 - Prob. 36PCh. 8.4 - Prob. 37PCh. 8.4 - Prob. 38PCh. 8.4 - Prob. 39PCh. 8.4 - Prob. 40PCh. 8.4 - Prob. 41PCh. 8.4 - Prob. 42PCh. 8.4 - Prob. 43PCh. 8.4 - Prob. 44PCh. 8.5 - Prob. 1PCh. 8.5 - Prob. 2PCh. 8.5 - Prob. 3PCh. 8.5 - Prob. 4PCh. 8.5 - Prob. 5PCh. 8.5 - Prob. 6PCh. 8.5 - Prob. 7PCh. 8.5 - Prob. 8PCh. 8.5 - Prob. 9PCh. 8.5 - Prob. 10PCh. 8.5 - Prob. 11PCh. 8.5 - Prob. 12PCh. 8.5 - Prob. 13PCh. 8.5 - Prob. 14PCh. 8.5 - Prob. 15PCh. 8.5 - Prob. 16PCh. 8.5 - Prob. 17PCh. 8.5 - Prob. 18PCh. 8.5 - Prob. 19PCh. 8.5 - Prob. 20PCh. 8.5 - Prob. 21PCh. 8.5 - Prob. 22PCh. 8.5 - Prob. 23PCh. 8.5 - Prob. 24PCh. 8.5 - Prob. 25PCh. 8.5 - Prob. 26PCh. 8.5 - Prob. 27PCh. 8.5 - Prob. 28PCh. 8.5 - Prob. 29PCh. 8.5 - Prob. 30PCh. 8.5 - Prob. 31PCh. 8.5 - Prob. 32PCh. 8.6 - Prob. 1PCh. 8.6 - Prob. 2PCh. 8.6 - Prob. 3PCh. 8.6 - Prob. 4PCh. 8.6 - Prob. 5PCh. 8.6 - Prob. 6PCh. 8.6 - Prob. 7PCh. 8.6 - Prob. 8PCh. 8.6 - Prob. 9PCh. 8.6 - Prob. 10PCh. 8.6 - Prob. 11PCh. 8.6 - Prob. 12PCh. 8.6 - Prob. 13PCh. 8.6 - Prob. 14PCh. 8.6 - Prob. 15PCh. 8.6 - Prob. 16PCh. 8.6 - Prob. 17PCh. 8.6 - Prob. 18PCh. 8.6 - Prob. 19PCh. 8.6 - Prob. 20PCh. 8.6 - Prob. 21PCh. 8.6 - Prob. 22PCh. 8.6 - Prob. 23PCh. 8.6 - Prob. 24PCh. 8.6 - Prob. 25PCh. 8.6 - Prob. 26PCh. 8.6 - Prob. 27PCh. 8 - Prob. 1SYUCh. 8 - Prob. 2SYUCh. 8 - Prob. 3SYUCh. 8 - Prob. 4SYUCh. 8 - Prob. 5SYUCh. 8 - Prob. 6SYUCh. 8 - Prob. 7SYUCh. 8 - Prob. 8SYUCh. 8 - Prob. 9SYUCh. 8 - Prob. 10SYUCh. 8 - Prob. 11SYUCh. 8 - Prob. 12SYUCh. 8 - Prob. 13SYUCh. 8 - Prob. 14SYUCh. 8 - Prob. 15SYUCh. 8 - Prob. 16SYUCh. 8 - Prob. 17SYUCh. 8 - Prob. 18SYUCh. 8 - Prob. 19SYUCh. 8 - Prob. 20SYUCh. 8 - Prob. 21SYUCh. 8 - Prob. 22SYUCh. 8 - Prob. 23SYUCh. 8 - Prob. 24SYUCh. 8 - Prob. 25SYUCh. 8 - Prob. 26SYUCh. 8 - Prob. 27SYUCh. 8 - Prob. 28SYUCh. 8 - Prob. 29SYUCh. 8 - Prob. 30SYUCh. 8 - Prob. 31SYUCh. 8 - Prob. 32SYUCh. 8 - Prob. 33SYUCh. 8 - Prob. 34SYUCh. 8 - Prob. 35SYUCh. 8 - Prob. 36SYUCh. 8 - Prob. 37SYUCh. 8 - Prob. 38SYUCh. 8 - Prob. 39SYUCh. 8 - Prob. 40SYUCh. 8 - Prob. 41SYUCh. 8 - Prob. 42SYUCh. 8 - Prob. 43SYUCh. 8 - Prob. 44SYUCh. 8 - Prob. 45SYUCh. 8 - Prob. 46SYUCh. 8 - Prob. 47SYUCh. 8 - Prob. 48SYUCh. 8 - Prob. 49SYUCh. 8 - Prob. 50SYUCh. 8 - Prob. 51SYUCh. 8 - Prob. 52SYUCh. 8 - Prob. 53SYUCh. 8 - Prob. 54SYUCh. 8 - Prob. 55SYUCh. 8 - Prob. 56SYUCh. 8 - Prob. 57SYUCh. 8 - Prob. 58SYUCh. 8 - Prob. 59SYUCh. 8 - Prob. 60SYUCh. 8 - Prob. 1FOTCh. 8 - Prob. 2FOTCh. 8 - Prob. 3FOTCh. 8 - Prob. 4FOTCh. 8 - Prob. 5FOTCh. 8 - Prob. 6FOTCh. 8 - Prob. 7FOT
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii a1=0.1 11. Consider the function f(x)=4x2(1x) a. Find any equilibrium points where f(x)=x. b. Determine the derivative at each of the equilibrium points found in part a. c. What does the theorem on the Stability of Equilibrium points tell us about each of the equilibrium points found in part a? d. Find the next four iterations of the function for the following starting values. i. a1=0.4. ii. a2=0.7 e. Describe the behavior of successive iteration found in part d. f. Discuss how the behavior found in part d relates to the results from part c.arrow_forwardThe cost (in dollars) of manufacturing one item is given by C(x, y) = 70 + 5x + 4y where x is the cost of 1 hour of labor and y is the cost of 1 pound of material. (a) If the hourly cost of labor is $16, and the material costs $3 per pound, what is the cost of manufacturing one of these items? $ (b) Find the partial derivative of C with respect to x. Cx Interpret the partial derivative of C with respect to x. O The cost (in dollars) of manufacturing one item will increase by $4 for a $1 increase in x if y is held constant. O The cost (in dollars) of manufacturing one item will increase by $5 for a $1 increase in x if y is held constant. The cost (in dollars) of manufacturing one item will increase by $4 for $1 increase in y if x is held constant. The cost (in dollars) of manufacturing one item will increase by $70 for a $1 increase in x if y is held constant. O The cost (in dollars) of manufacturing one item will increase by $5 for a $1 increase in y if x is held constant.arrow_forward(8) Find dz if the equation yz – In z = x² +y² defines z as a function of two independent variables r and and partial derivative exists.arrow_forward
- The cost (in dollars) of manufacturing one item is given by C(x, y) = 10 + 9x + 7y where x is the cost of 1 hour of labor and y is the cost of 1 pound of material. (a) If the hourly cost of labor is $23, and the material costs $3 per pound, what is the cost of manufacturing one of these items? $ (b) Find the partial derivative of C with respect to x. Cx = Interpret the partial derivative of C with respect to x. O The cost (in dollars) of manufacturing one item will increase by $9 for a $1 increase in x if y is held constant. O The cost (in dollars) of manufacturing one item will increase by $9 for a $1 increase in y if x is held constant. O The cost (in dollars) of manufacturing one item will increase by $7 for a $1 increase in y if x is held constant. ○ The cost (in dollars) of manufacturing one item will increase by $7 for a $1 increase in x if y is held constant. The cost (in dollars) of manufacturing one item will increase by $10 for a $1 increase in x if y is held constant.arrow_forward. Find the second partial derivatives of f(x, y) = 2x² + 3x³y + 2x³y²arrow_forwardIf f is a function of three variables that has continuous second-order partial derivatives, then div(Vf) (i) does not make sense (ii) makes sense and is always zero (iii) makes sense and may be nonzeroarrow_forward
- Find the second order partial derivatives of f(x.y)-(3x+2y)*4* O Option 4 O Option 2 Option O Option 3arrow_forwardIf f is a function of three variables that has continuous second-order partial derivatives, then curl(Vf) (i) does not make sense (ii) makes sense and is always zero (iii) makes sense and may be nonzero SEarrow_forwardBoth first partial derivatives of the function f(x,y) are zero at the given points. Use the second-derivative test to determine the nature of f(x,y) at each of these points. If the second-derivative test is inconclusive, so state. f(x,y) = - 9x + 18xy - y° +81y; (- 3, – 3), (9,9) What is the nature of the function at (- 3, - 3)? A. f(x,y) has a relative minimum at (- 3, - 3). B. f(x,y) has neither a relative maximum nor a relative minimum at (- 3,– 3). C. f(x,y) has a relative maximum at (- 3, - 3). D. The second-derivative test is inconclusive at (- 3, - 3). What is the nature of the function at (9,9)? A. f(x,y) has a relative minimum at (9,9). B. f(x,y) has neither a relative maximum nor a relative minimum at (9,9). C. f(x,y) has a relative maximum at (9,9). D. The second-derivative test is inconclusive at (9,9). O Oarrow_forward
- Find the four second partial derivatives of the following function f(xy)-In (7x2 + y2 +9)arrow_forwardIn substituting the point (4,1,2) in the partial derivatives, why does the terms without x and y becomes zero?arrow_forwardFind the following higher order partial derivatives. (A) (B) 8²% дхду (C) 8²% əx² || x³ + y² + z² = 5 8²% მყ2 (Note that your answers should be a function of x, y and z.)arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
Calculus For The Life Sciences
Calculus
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:Pearson Addison Wesley,
08 - Conic Sections - Hyperbolas, Part 1 (Graphing, Asymptotes, Hyperbola Equation, Focus); Author: Math and Science;https://www.youtube.com/watch?v=Ryj0DcdGPXo;License: Standard YouTube License, CC-BY