Gradient Vector- largest possible rate of change?

[Jason Sylvestre]

Hello,

My professor just gave us a True or False problem that states:

∇H(x,y), the gradient vector of H(x,y), gives us the largest possible rate of change of H at (x,y).

Now, he said the answer is true, but it was my understanding that the gradient itself gives the direction of where the function increases fastest. And then in order to find the maximum rate of change, you have to find the magnitude of the gradient vector and plug in the point to the function.

Is there some flaw in my understanding?

Thanks

 

[Orodruin]

The gradient contains information on both the direction and maximal rate of change. The magnitude is a property of a vector.