Write up the following problem neatly and completely! Explain your strategy or r
ID: 2888474 • Letter: W
Question
Write up the following problem neatly and completely! Explain your strategy or reasoning. Your score is based on both the correctness and the presentation of your solution. 4 A portion of a contour map for a function f is shown. Each level curve f(x,y)= k is labeled with the corresponding value of k. Determine whether each of the following partial derivatives is positive or negative at the point indicated on the contour map. You must explain your reasoning, not just give the answer! (a) (b), (c) for (d)hy 5. (e) yExplanation / Answer
a) If we start to walk from the given dot say it is P towards parallel to the +ve direction of X axis, we will reach level curve k=5. And as our pint P lies between k=4 and k=5 (Let P lies on k=Pk), we have fx=(5-pk)/(increment of x), it is +ve.
b) If we start to walk from the given dot say it is P towards parallel to the +ve direction of Y axis, we will reach level curve k=4. And as our pint P lies between k=4 and k=5 (Let P lies on k=Pk), we have fx=(4-pk)/(increment of y), it is -ve.
c) Again let us start from fx way and see that level curves are moving far from each other. Therefore fxx is -ve.
d) Next let us start from fy way and see that level curves are coming close to each other. Therefore fyy is +ve.
e) Keeping fix fx line parallel to the +ve direction of X axis if we move up, we will find again the level curves are coming closer. Therefore fxy is +ve.
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