# Rate of change problem

1. Jul 17, 2006

### teng125

potential V at the point P(2, -1, 2) in a rectangular
coordinate system is V (x, y, z) =x^2+4y^2+9z^2.

Find the direction that produces the maximum rate of change of V at P.

the max rate of change 37.094.
how to find direction that produces the maximum rate of change ??

2. Jul 17, 2006

### Staff: Mentor

3. Jul 17, 2006

### HallsofIvy

Staff Emeritus
Also, if f is in x,y,z coordinates, then $\nabla f= \frac{\partial f}{\partial x}+ \frac{\partial f}{\partial y}+ \frac{\partial f}{\partial z}$.

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