B2: Partial Derivatives

Drag to rotate view. Click on surface to move point.
Arrow keys nudge position. R to reset view.

💡 This bowl-shaped surface has minimum at the origin. Both partial derivatives are zero there!

Function:
f(x,y) = ¼(x² + y²)
∂f/∂x = ½x
∂f/∂y = ½y
Position (x, y) 1.00, 1.00
Height f(x,y) 0.50
∂f/∂x
0.50 ↗ Rising
Slope along RED slice (y held constant)
∂f/∂y
0.50 ↗ Rising
Slope along BLUE slice (x held constant)