Why is \nablaf in the Direction of Steepest Ascent?

[icystrike]

Homework Statement

I am wondering why \nablaf is along the direction of steepest ascend.

Homework Equations

The Attempt at a Solution

No idea..

 

[Inferior89]

The derivative of f in direction \mathbf{u} (\mathbf{u} is a unit vector) is
\nabla f \cdot \mathbf{u} = |\nabla f||\mathbf{u}|\cos \theta.
This has a maximum when \theta = 0 which means that \mathbf{u} points in the same direction as \nabla f \cdot

The maximum value of the derivative is thus |\nabla f| in the direction \nabla f.

 

[icystrike]

Thanks inferior! got that.. =D