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

Section 4.5: Gradient Vector

Example 4.5.1

Let fx,y=52 x23 y2 and let P be the point 1,2.


Obtain f at P.


Graph the surface z=fx,y.


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


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


At P, obtain ψ=f·u, the directional derivative of f in the direction u=cost i+sint j . Show that ψ is a maximum when u is along fP and that this maximum is fP.

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