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Mathematics 107 Online
OpenStudy (anonymous):

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

OpenStudy (anonymous):

my bad i have D_vf(P)=4

OpenStudy (jamesj):

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

OpenStudy (anonymous):

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!

OpenStudy (jamesj):

Definitely need to normalize.

OpenStudy (anonymous):

cool thanks man!

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