Question

Should this be in 2 or 3 dimensions?

Answer 1

\[f(x,y,z)=x^6+y^3+y^4\]And the lack of z term is not a typo.
I'm confused. Should the gradient of this function be \[grad(f)=(6x^5,3y^2+4y^3)\] or\[grad(f)=(6x^5,3y^2+4y^3,0)\]

Answer 2

i dont know this topic well, but i would assume it would be the second answer because based on the notation f(x,y,z) they want all 3 parts, and they likely know that z=0

Answer 3

Yes, that's what I was thinking, too. The lack of any z terms in the function had me confused.

Answer 4

like i said, i dont know this subject, but in math, it really doesnt matter much if theres a 0 for most applications
example
complex numbers
4+0i is the same as 4