Calculating Rate of Change
At the point (0,1,2) in which direction does the function increase most rapidly? What is the rate of change of in this direction? At the point (1,1,0), what is the derivative of in the direction of the vector ?
I assumed that the rate of change is the same as the gradient of the function, namely . Calculating this gave me:
Evaluating at point:
Hence, the function increases most rapidly in the x direction.
I am uncertain of how to approach solving the third part of the question, should I evaluate the rate of change at (1,1,0) and then find the difference between that and the vector ?