Example 4-5-1 - Maple Help
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Chapter 4: Partial Differentiation

Section 4.5: Gradient Vector

Example 4.5.1

Let  and let P be the point .

a) 

Obtain  at P.

b) 

Graph the surface .

c) 

On the same set of axes, graph the level curve through P, and  at P.

d) 

At P, show that  is orthogonal to a vector tangent to the level curve through P.

e) 

At P, obtain , the directional derivative of  in the direction  . Show that  is a maximum when u is along  and that this maximum is .

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