Maximal Directional Derivative of the Function - Indicate Limits of Integration - Mathematics Assignment Help

Assignment Task :

Question 1 

 A surface in space is defined by the following equation:

a) Find the equation of the tangent plane to the surface at the point P(0, -1). Present your answers in the exact form for full marks. 

b) Find the maximal directional derivative of the function z(x,y) at point P and give the direction in which it is maximum. 

Question 2 

Find all critical points of the function: 

and determine their character, that is whether there is a local maximum, local minimum, saddle point or none of these at each critical point. 

Question 3 

Consider the double integral: 

a) Sketch the region over which the integration is being performed.

b) Reduce the integral to polar coordinates and indicate limits of integration.

c) Calculate the integral and present your answer with four significant figures

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