Question

Find a unit vector U such that the rate of change of f in the direction of U at the given point is maximum.

point being (3,5,pi)

I know hos to do this when given a direction but since im asked to ind the unit vector first it kinda throws me off. do i just use my point? like make it a vector and divide by it's absolute value so i get a unit vector. would that be in the same direction of ∇f so i can get a max?

Answer 1

<3,5,pi>*(1/(106+pi^2)^(1/2)

Answer 2

You would just want to find the unit vecter like you had said in the first place.