i dont understand why dz/dy will be zero instead of positive...P goes up it beco

Question

i dont understand why dz/dy will be zero instead of positive...P goes up it become 6 to 7, why dz/dy still zero?

Also, how can i find the slope of d2z/dx2 and d2z/dy2 here?? how to do this?

3. f(x, y) is a smooth continuous function whose level curves are shown below. min Sade pol 4 i n 2 1 2 345 6 78 9 Use this graph to answer the following questions. You do not need to show work. (a) 1 point eachl At the point P, indicate whether the following partial derivatives are positive, negative, or zero. (Circle your answers.) : Positive NegativeZero PositiveNegative Zero 2 : Positive Negative (Zero Positive) Negative Zero 2

Explanation / Answer

while calculating dz/dx we take a very small step in x direction . with very little change in x we see that we move out of the given curve . so the z value decrease. so dy/dz = negetive

while calculating dz/dy we take a very small step in y direction . with very little change in y we see that its the part of the curve. so the z value remains the same. so dy/dz =0

if you image the above figure as a 3D image, the you can find out the the curves are concave upwards in both x and y directions. so the second order partial derivatives are both positive

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