Question

Is there a typo in Session 38's Solution Guide?

Answer 1

http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/2.-partial-derivatives/part-b-chain-rule-gradient-and-directional-derivatives/session-38-directional-derivatives/MIT18_02SC_pb_45_comb.pdf

They compute T-gradient = <2x, 4y, 4z>, but then say that T-gradient at the point <1, 1, 1> = <1, 2, 2>... shouldn't this be <2, 4, 4>?

This would make the solution to part (b), 1/2 the given answer (0.05 instead of 0.1).

Thoughts?
Thanks!
-Gene

Answer 2

good catch.
they are correct to claim -<1,2,2> is the direction of fastest decrease, but they should not ignore the scale factor of 2 when computing the numerical value of the decrease (i.e. the length of the gradient vector evaluated at the given point).

Answer 3

Thanks Phi :)