### Function Festival Fall 2000

# Dawn Ehlers, Math Artist

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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.

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