Question

could someone tell me if this is right?

question:
compute the directional derivative of the function f(x,y,z)=zx-xy^2 at P = (1,1,1) in the direction of v = <2,-1,2>

my answer:
D_uf(P)=4/3
is that right?
could someone tell me if this is right?

question:
compute the directional derivative of the function f(x,y,z)=zx-xy^2 at P = (1,1,1) in the direction of v = <2,-1,2>

my answer:
D_uf(P)=4/3
is that right?
@Mathematics

Answer 1

my bad i have
D_vf(P)=4

Answer 2

Div f = (z - y^2, -2xy, x)
and at P = (1,1,1) Div f = (0,-2,1)

Now normalizing v, write it as w = v/||v|| = 1/3 (2,-1,2)

Hence D_v f (P) = div f(P) . w = (0,-2,1) . 1/3 (2,-1,2) = 1/3 (2 + 2) = 4/3.

So I think you forgot to normalize the direction vector v

Answer 3

ok yeah thats how i did it at first but then i wasnt sure if i had to normalize the vector, but i guess i do...thanks James!

Answer 4

Definitely need to normalize.

Answer 5

cool thanks man!