The Gradient Vector

3D Perspective

+∇f Steepest Ascent

−∇f Steepest Descent

Gradient on xy-plane

Surface Function

f(x,y) = 0.25(x² + y²)

∇f = [0.5x, 0.5y]

💡 The gradient always points away from the minimum at (0,0). Watch it shrink to zero as you approach!

Negative Gradient

Partial Components

Show xy-Plane Gradient

Learning Rate (α) 0.10

Click anywhere on surface to place point