Function Festival Fall 2000

Dawn Ehlers, Math Artist


Surface: z = 6-(x/8)^2-(y/8)^2
at points: A = (4,6,5.1875), B = (0,16,2)


The vector from pt. A to pt. B is <-4,10>.


The slope in the direction of x, (fx(x,y)), is -x/32.
The slope in the direction of y, (fy(x,y)), is -y/32.


The gradient of f(x,y) = z is -(1/32)(xi+yj).
The gradient of f(4,6) = z is -(1/16)(2i+3j).


The unit vector from pt. A to pt.B is
u = (1/116)^(1/2)(-4i+10j).


The directional derivative of z at (-1,-1) in
the direction of u is
(1/116)^(1/2)(-4i+10j) . -(1/16)(2i+3j)
= -0.1276695545.



Dawn 1

Dawn 2

Dawn 3

Dawn 4


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