Vectors, Gradients and Rate of Change
8. The Intergalactic Ship Zora is hanging motionless at (5, 1, 10) (Universal Galatic Coordinates) when the crew spots an interesting object at (7, 5, 6). The temperature in that part of the galaxy is given by T(x,y,z) = x2 + y/x + z3. As the crew starts to move the Zora directly toward the unknown object, what is the rate of change in temperature?