use x and y · functions: sin, cos, tan, sqrt, log, exp, abs · constants: pi, e · ^ for power
3d surface · z = f(x, y)
paraboloid
cutting plane: 0.00
cutting plane z = c
contour where f(x, y) = c
drag to rotate · scroll to zoom
at probe (drag the orange dot on the map)
(x, y)(0.00, 0.00)
∂f/∂x0.00
∂f/∂y0.00
|∇f| = √(fx² + fy²)0.00
direction u (drag the teal handle)
angle of u0°
Du f = ∇f · u+0.00
dx
dy
df
u
2d contour map · steep = lines crowd together
level set: f(x, y) = 0.00
other level lines
current level (matches plane)
steepness |∇f| · brighter rose = steeper
probe · drag me
∇f points uphill, ⟂ to contour
direction u · drag teal tip to rotate
⟂ from ∇f tip to u-line · projection foot
Duf as projected length
∇f
u
Duf