Region

1. The Bowl

f(x,y) = x^2 + y^2

Critical points 0 / 1

Valley = local minimum Peak = local maximum Pass = saddle point

Second-derivative test D = fxx*fyy - fxy^2 D > 0 and fxx > 0: min D > 0 and fxx < 0: max D < 0: saddle

position(0.00, 0.00)

height f0.00

fx0.00fy0.00

|grad f|0.00

WASD / arrows to walk · drag to orbit · wheel to zoom

Field Survey · Multivariable Calculus

PEAK HUNTER

Walk across z = f(x, y). The glowing arrow points uphill, which is the gradient. When the ground goes flat, use the Hessian test to classify the point as a valley, peak, or saddle.

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Rotate to landscape for the cleanest Peak Hunter controls.