You are standing above the point 23 on the surface z 30 3x

You are standing above the point (2,3) on the surface z = 30 - (3x^2 + y^2). In which direction should you walk to descend fastest? (Give your answer as a unit 2-vector.) direction = If you start to move in this direction, what is the slope of your path? slope =

Solution

BY taking the derivative

-6xi - 2yj, at the point (2,3) it will become

-12i - 6j

b) Slope of your path = ||delta f(2,3)|| = sqrt((12)^2 + (6)^2)) = sqrt(144+36) = sqrt(180) = 13.41 units