### Function Festival Fall 2000

# Eoi Kim, Math Artist

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Find the directional derivative of:

z=11-.2x^(2)-(y^(2)/5) at (2,-6,3) in the direction

from A(2,-6,3) to B(4,-3,6).

We have the function f(x,y)=11-.2x^2-(y^2)/5, so

we must find AB. AB=(4-2)i+(-3+6)j=2i+3j

and we can find the unit vector u= v/(IIvII).

So u=2/(13^(1/2))i+3/(13^(1/2)j=(.5547i+.8321j)

grad f(x,y)=fx(x,y)i+fy(x,y)j=.4x^(.5)i+(2y)/5j

Then the direction of derivative at (2,-6)

Duf(2,-6)=grad f(2,-6)*u

=(.8i+2.4j)(.5547i+.8321j)

=(.44376+1.99704)

=2.4408

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