The Gradient

The direction of steepest ascent

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• $\nabla f = (\partial f/\partial x, \partial f/\partial y)$ points in the direction of steepest ascent.
• The gradient is perpendicular to contour lines.
• Its length $|\nabla f|$ is the steepest slope. At peaks it's zero.

Steps

1. An arrow pointing uphill
2. Along a contour
3. Walking diagonally
4. Steepest climb
5. A lopsided hill
6. Steepness