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