Maximum value of directional derivative (Duf)?

[JC3187]

Hi guys,

I am confused from what I know the max. value of directional derivative at a point is the length of the gradient vector ∇f or grad. f?

Why does the answer in my book of a question say that
Max. val of Duf = (√3145)/5
when ∇f = (56/5) i- (3/5) j
?

Thanks

 

[pasmith]

Hi guys,

I am confused from what I know the max. value of directional derivative at a point is the length of the gradient vector ∇f or grad. f?

Why does the answer in my book of a question say that
Max. val of Duf = (√3145)/5
when ∇f = (56/5) i- (3/5) j
?

Thanks

$$\|\nabla f\| = \sqrt{\left(\frac{56}{5}\right)^2 + \left(-\frac{3}{5}\right)^2} = \dots$$

 

[HallsofIvy]

It is the difference between "a vector" and "length of a vector".