Function Festival Fall 2000

Per Kim, Math Artist

my fuction is z=6-(1/2)(x^2)-(1/8)(y^2)

and my points are P(3,-3,3/8) R(0,0,6)

then I can find the vector V=(-3,3)

and unit vector U= V/IIVII


because grad f(x,y)=fx(x,y)i+fy(x,y)j is

grad f(x,y)= -xi-(1/4)y

grad f(3,-3) = -3i-(3/4)

consequently, at (3,-3,3/8) the directional
derivatiive is

Duf(x,y)= (-3)(-1/(2)^(1/2))+(3/4)(1/(2)^(1/2))
= (12+3)/(4(2)^(1/2))

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