### 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

U=(1/(3(2)^(1/2))(-3i+3j)

=(1/(2)^(1/2))(-i+j)

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))

=(15(2)^(1/2))/8

Other Math Artists

Other FUNctions

Function Festival Story Board