For the function defined as follows, find all values of x and y such that both fx(x,y) = 0 and fy (x,y) = 0. f(x,y) = 5x² + 7y² + 3xy + 33x - 2 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. There is only one solution where f(x,y) = 0 and f(x,y) = 0, when x = and y = O A. (Type integers or simplified fractions.) and y= O B. There are two solutions where fx(x,y) = 0 and f, (x,y) = 0, in order from increasing x values, when x = (Type integers or simplified fractions.) and y= OC. There are three solutions where f(x,y) = 0 and fy(x,y) = 0, in order from increasing x values, when x = | x= and y=. (Type integers or simplified fractions.) D. There are no solutions where fx (x,y) = 0 and f, (x,y) = 0. and x = and x = and y = and y = and
For the function defined as follows, find all values of x and y such that both fx(x,y) = 0 and fy (x,y) = 0. f(x,y) = 5x² + 7y² + 3xy + 33x - 2 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. There is only one solution where f(x,y) = 0 and f(x,y) = 0, when x = and y = O A. (Type integers or simplified fractions.) and y= O B. There are two solutions where fx(x,y) = 0 and f, (x,y) = 0, in order from increasing x values, when x = (Type integers or simplified fractions.) and y= OC. There are three solutions where f(x,y) = 0 and fy(x,y) = 0, in order from increasing x values, when x = | x= and y=. (Type integers or simplified fractions.) D. There are no solutions where fx (x,y) = 0 and f, (x,y) = 0. and x = and x = and y = and y = and
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 48CR
Related questions
Question
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**Problem Statement:**
For the function defined as follows, find all values of \(x\) and \(y\) such that both \(f_x(x,y) = 0\) and \(f_y(x,y) = 0\).
\[f(x,y) = 5x^2 + 7y^2 + 3xy + 33x - 2\]
---
**Question:**
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
- **A.** There is only one solution where \(f_x(x,y) = 0\) and \(f_y(x,y) = 0\), when \(x =\) \_\_\_\_ and \(y =\) \_\_\_\_.
(Type integers or simplified fractions.)
- **B.** There are two solutions where \(f_x(x,y) = 0\) and \(f_y(x,y) = 0\), in order from increasing \(x\) values, when \(x =\) \_\_\_\_ and \(y =\) \_\_\_\_ and \(x =\) \_\_\_\_ and \(y =\) \_\_\_\_.
(Type integers or simplified fractions.)
- **C.** There are three solutions where \(f_x(x,y) = 0\) and \(f_y(x,y) = 0\), in order from increasing \(x\) values, when \(x =\) \_\_\_\_ and \(y =\) \_\_\_\_ and \(x =\) \_\_\_\_ and \(y =\) \_\_\_\_ and \(x =\) \_\_\_\_ and \(y =\) \_\_\_\_.
(Type integers or simplified fractions.)
- **D.** There are no solutions where \(f_x(x,y) = 0\) and \(f_y(x,y) = 0\).
---
**Note:**
Students are required to select and fill in the appropriate values for \(x\) and \(y\) based on the calculus problem involving partial derivatives set to zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F756689fc-aa25-4045-a342-f553545a40f2%2Fa4789a7c-e57b-48eb-8335-3cb0dd1872b7%2F43i399_processed.png&w=3840&q=75)
Transcribed Image Text:---
**Problem Statement:**
For the function defined as follows, find all values of \(x\) and \(y\) such that both \(f_x(x,y) = 0\) and \(f_y(x,y) = 0\).
\[f(x,y) = 5x^2 + 7y^2 + 3xy + 33x - 2\]
---
**Question:**
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
- **A.** There is only one solution where \(f_x(x,y) = 0\) and \(f_y(x,y) = 0\), when \(x =\) \_\_\_\_ and \(y =\) \_\_\_\_.
(Type integers or simplified fractions.)
- **B.** There are two solutions where \(f_x(x,y) = 0\) and \(f_y(x,y) = 0\), in order from increasing \(x\) values, when \(x =\) \_\_\_\_ and \(y =\) \_\_\_\_ and \(x =\) \_\_\_\_ and \(y =\) \_\_\_\_.
(Type integers or simplified fractions.)
- **C.** There are three solutions where \(f_x(x,y) = 0\) and \(f_y(x,y) = 0\), in order from increasing \(x\) values, when \(x =\) \_\_\_\_ and \(y =\) \_\_\_\_ and \(x =\) \_\_\_\_ and \(y =\) \_\_\_\_ and \(x =\) \_\_\_\_ and \(y =\) \_\_\_\_.
(Type integers or simplified fractions.)
- **D.** There are no solutions where \(f_x(x,y) = 0\) and \(f_y(x,y) = 0\).
---
**Note:**
Students are required to select and fill in the appropriate values for \(x\) and \(y\) based on the calculus problem involving partial derivatives set to zero.
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