Why is \nablaf in the Direction of Steepest Ascent?

[icystrike]

Homework Statement

I am wondering why $$\nabla$$f 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