{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Gilbert_Hmwk13sol - moseley(cmm3869 HW13 Gilbert(56380 This...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
moseley (cmm3869) – HW13 – Gilbert – (56380) 1 This print-out should have 26 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Determine f x + f y when f ( x, y ) = 2 x 2 2 xy + 2 y 2 + x + 3 y . 1. f x + f y = 6 x + 2 y 2 2. f x + f y = 6 x 6 y 2 3. f x + f y = 2 x + 2 y + 4 correct 4. f x + f y = 2 x + 2 y 2 5. f x + f y = 2 x 6 y + 4 6. f x + f y = 6 x 6 y + 4 Explanation: After differentiation we see that f x = 4 x 2 y + 1 , f y = 2 x + 4 y + 3 . Consequently, f x + f y = 2 x + 2 y + 4 . 002 10.0 points From the contour map of f shown below decide whether f x , f y are positive, negative, or zero at P . 0 0 2 2 4 4 6 6 P x y 1. f x < 0 , f y < 0 2. f x > 0 , f y = 0 3. f x > 0 , f y < 0 correct 4. f x < 0 , f y > 0 5. f x > 0 , f y > 0 6. f x < 0 , f y = 0 Explanation: When we walk in the x -direction from P we are walking uphill, so f x > 0. On the other hand, when we walk in the y -direction from P we are walking downhill, so f y < 0. Consequently, at P f x > 0 , f y < 0 . keywords: contour map, slope, partial deriva- tive, 003 10.0 points Determine whether the partial derivatives f x , f y of f are positive, negative or zero at the point P on the graph of f shown in P x z y
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
moseley (cmm3869) – HW13 – Gilbert – (56380) 2 1. f x < 0 , f y = 0 2. f x = 0 , f y > 0 3. f x < 0 , f y > 0 correct 4. f x > 0 , f y > 0 5. f x = 0 , f y < 0 6. f x = 0 , f y = 0 7. f x < 0 , f y < 0 8. f x > 0 , f y = 0 Explanation: The value of f x at P is the slope of the tangent line to graph of f at P in the x - direction, while f y is the slope of the tangent line in the y -direction. Thus the sign of f x indicates whether f is increasing or decreasing in the x -direction, or whether the tangent line in that direction at P is horizontal. Similarly, the value of f y at P is the slope of the tangent line at P in the y -direction, and so the sign of f y indicates whether f is increasing or decreasing in the y -direction, or whether the tangent line in that direction at P is horizontal. From the graph it thus follows that at P f x < 0 , f y > 0 . keywords: surface, partial derivative, first or- der partial derivative, graphical interpreta- tion 004 10.0 points Determine f x when f ( x, y ) = 2 x y x + 2 y . 1. f x = 4 y ( x + 2 y ) 2 2. f x = 3 x ( x + 2 y ) 2 3. f x = 4 x ( x + 2 y ) 2 4. f x = 3 y ( x + 2 y ) 2 5. f x = 5 y ( x + 2 y ) 2 correct 6. f x = 5 x ( x + 2 y ) 2 Explanation: From the Quotient Rule we see that f x = 2( x + 2 y ) (2 x y ) ( x + 2 y ) 2 . Consequently, f x = 5 y ( x + 2 y ) 2 . 005 10.0 points Find the slope in the x -direction at the point P (0 , 2 , f (0 , 2)) on the graph of f when f ( x, y ) = 2( y 2 x 2 ) ln( x + y ) . 1. slope = 4 correct 2. slope = 6 3. slope = 8 4. slope = 0 5. slope = 2 Explanation: The graph of f is a surface in 3-space and the slope in the x -direction at the point P (0 , 2 , f (0 , 2)) on that surface is the value of the partial derivative f x at (0 , 2). Now f x = 2 parenleftbigg 2 x ln( x + y ) + y 2 x 2 x + y parenrightbigg .
Image of page 2
moseley (cmm3869) – HW13 – Gilbert – (56380) 3 Consequently, at P (0 , 2 , f (0 , 2)) slope = 2 × 2 = 4 .
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern