BOT 2100 Lecture : Flowers and floral organ identity genes

Let F=〈8xyz+3sinx,4x2z,4x2y〉F=〈8xyz+3sin⁡x,4x2z,4x2y〉. Find a function ff so that F=∇fF=∇f, and f(0,0,0)=0f(0,0,0)=0.

For each of the following vector fields FF, decide whether it is conservative or not by computing curl FF. Type in a potential function ff (that is, ∇f=F∇f=F). Assume the potential function has a value of zero at the origin. If the vector field is not conservative, type N.

F(x,y,z)=6xi+7yj+k
f(x,y,z)=f(x,y,z)=

equation editor

Equation Editor

D. F(x,y)=(6siny)i+(−6y+6xcosy)j
f(x,y)=