1. The problem statement, all variables and given/known data Captain Ralph is in trouble near the sunny side of Mercury. The temperature of the ship's hull when he is at location (x; y; z) will be given by T=e^(-x²-2y²-3z²). He is currently at (1,1,1). a)In which direction should Ralph go to cool the fastest? b) If the ship can travel at a speed of e^8, what will be the rate of cooling? 2. Relevant equations 3. The attempt at a solution a) The direction he should go would be the negative of the gradient, which I got to be (2e^-6, 4e^-6, 5e^-6). Easy. b) Here's where I got lost. the answers online (source http://www.cds.caltech.edu/~marsden/wiki/uploads/math1c-08/assignments/homework_sol3.pdf) say just take the gradient and multiply it by the speed. My question is, shouldn't we need to take a unit vector in the direction of the gradient?