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Contour diagram and second order of partial derivative

  1. Feb 24, 2009 #1
    1. The problem statement, all variables and given/known data
    The following contour diagram represents the function z = f(x,y)

    http://img15.imageshack.us/img15/9059/contour.th.jpg [Broken]

    (a) Is z an increasing or decreasing function of x?
    I'd say it's increasing as it goes towards the x-axis the contour lines value goes down
    (b) Is z an increasing or decreasing function of y?
    I'd say it's decreasing as it goes towards the y-axis the contour lines value goes down
    (c) Is fxx positive or negative?
    I think it's negative
    (d) Is fyy positive or negative?
    I think it's negative
    (e) Is grad f longer at point P or Q?
    Q

    Is my answer correct?
    2. Relevant equations



    3. The attempt at a solution
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Feb 24, 2009 #2

    Dick

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    I'd agree with all of your answers. I'm I little confused about the reasoning on some of them. E.g. for a) I'd say it's an increasing function of x because z is increasing as you move away from the y-axis. Oh, I think I see what you mean. You mean f is increasing as you move ALONG the x-axis.
     
  4. Feb 24, 2009 #3
    I just tried my answer and c) is supposed to be positive why is this?
     
  5. Feb 24, 2009 #4

    Dick

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    Yeah, you're right. Sorry. As you move along the x-axis from a point z is increasing at an increasing rate since the contours are spaced closer together as you move in the positive x direction. I guess I wasn't paying close attention. Sorry again. Also think I might have been asleep at the wheel for e). The magnitude of grad is proportional to the maximum rate of change at a point, right? Closer contours mean faster rate of change.
     
  6. Feb 24, 2009 #5
    and why is the answer to part e) P?
     
  7. Feb 24, 2009 #6

    Dick

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    I already realized I'd been dozing. See the answer above. Sorry again.
     
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