## Proof That a Function f Changes Most Rapidly in the Direction of Grad f

Theorem

A functionchanges most rapidly in the direction of

Proof

Ifand then sinceis a unit vector.

whereis the angle betweenand

Noteis a unit vector.

Henceis greatesat whenand

Theorem

A functionchanges most rapidly in the direction of

Proof

Ifand then sinceis a unit vector.

whereis the angle betweenand

Noteis a unit vector.

Henceis greatesat whenand