Hi, I'm looking at the questions on directional derivatives set for session 38 in the 18.02sc course. We're given T=x^2 + 2y^2 + 2z^2 and asked to find the direction for maximum decrease in T at P=(1,1,1) and the directional derivative in this direction. I agree with the published answer that the direction is unit vector u=. I see grad P at T as =, so I get the directional derivative as .=6. But the published answer is 3; am I being an idiot?

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Hi, I'm looking at the questions on directional derivatives set for session 38 in the 18.02sc course. We're given T=x^2 + 2y^2 + 2z^2 and asked to find the direction for maximum decrease in T at P=(1,1,1) and the directional derivative in this direction. I agree with the published answer that the direction is unit vector u=<-1/3,-2/3,-2/3>. I see grad P at T as <2x,4y,4z>=<2,4,4>, so I get the directional derivative as <2,4,4>.<-1/3,-2/3,-2/3>=6. But the published answer is 3; am I being an idiot?