Multivariable Vector: Gradient @ particular speed - Find Rate

1. Apr 3, 2012

MJSemper

1. The problem statement, all variables and given/known data
Given: Concentration of Fluid = F(x,y,z) = 2x^2 + 4y^4 + 2*x^2*z^2 at point (-1,1,1)
----If you start to move in the direction of Grad(F) at a speed of 8, how fast is the concentration changing?

2. Relevant equations

...at point (-1,1,1) = < -8,16,4 >

3. The attempt at a solution

I know that the gradient is the direction of greatest change, and its magnitude is the particular rate thereof. What I'm stuck at is how the "speed of 8" plays in there. Is it a scalar value to the magnitude of the gradient vector?

I guess you should calculate $$\frac{dF}{dt} = \nabla F \cdot \frac{d\mathbf{x}}{dt}$$