Directional Derivative

[e^x]

I found that grad w = < y + z, x + z, y + x >

grad w (1, -1, 2) = <1, 3, 0>

length of grad w (1, -1, 2) is sqrt(10), the maximum value

How do I find the minimum value?

 

[blamocur]

I am assuming that [imath]\frac{df}{ds}|_u[/imath] means derivative of [imath]f[/imath] over the length [imath]s[/imath] in the direction [imath]u[/imath]. It is easily derived from the gradient and the unit vector [imath]u[/imath] -- do you know how ?

 

[e^x]

I am assuming that [imath]\frac{df}{ds}|_u[/imath] means derivative of [imath]f[/imath] over the length [imath]s[/imath] in the direction [imath]u[/imath]. It is easily derived from the gradient and the unit vector [imath]u[/imath] -- do you know how ?

I know how to find the directional derivative in the direction of unit vector u, but it doesn't specify what u is so what do I do

 

[Dr.Peterson]

Look at how you find the directional derivative, and think about what direction will maximize it. That is the direction they want!

 

[blamocur]

I know how to find the directional derivative in the direction of unit vector u, but it doesn't specify what u is so what do I do

9.b explicitly asks you to find which [imath]u[/imath]'s correspond to the minimum and the maximum derivatives. What is your formula for the directional derivative corresponding to an arbitrary [imath]u[/imath]?