Confused about a practice problem on the directional derivatives session.
The function T = x^2 + 2*y^2 + 2*z^2
gives the temperature at each point in space.
1. At the point P = (1,1,1), in which direction should you go to get the most rapid decrease in T? What is the directional derivative in this direction?
So I get ∇T = <2x,4y,4z> and ∇T = <2,4,4> at P=(1,1,1). So the direction opposite ∇T gives the greatest magnitude. Let u be a unit vector in this direction.
dT/ds|u = |∇T|*|u|*cosθ = 6*1*(-1) = -6
But the solution says that -∇T=-<1,1,2> at P=(1,1,1) and that dT/ds|u = -3.
They also compute u=-<1/3,2/3,2/3>

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