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?

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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?

MIT 18.02 Multivariable Calculus, Fall 2007
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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