answer the following questions

65536 assignment
Given function Z is in two variables. So we use partial derivatives method. We find first two derivatives as follows:
To find maxima, equate first derivative to 0 and solve
8x-2y =28 and 2x-6y =18
Solving we get (x,y) = (3,-2)
Let us calculate D now
Since zxx depends on h0 value if h0 is positive then Z is maximum at (3,-2)
Maximum distance is at x=3 and y =-2 provided h0 >0
b) Maximum peak = Z(3,-2) =
Maximum peak = 72 units
c) If we have to select the steepest path, then direct vertical only will be the steepest path.
So the path should be along the straight line connecting (3,2,72) a point in the xy plane.
When z=0, we have the equation of an ellipse on xy plane.
Let us write this as a function of 3 variables
Let us find gradient of this function.
Gradient is maximum steepness.
Hence the path should b across this.
Substitute (x,y) = (3,-2)
We get gradient = (-4-24+28, 6+12+28,-1) = (0, 46,-1)
So the path...