Consider the vector field f(x, y,z)=(4z+5y)i+(4z+5x)j+(4y+4x)k. a. find a function f such that f=∇f and f(0,0,0)=0.

The gradient of a function f, denoted as ∇f , is the collection of all its partial derivatives into a vector.

Function  

Gradient of vector field is given by,

And function is given that,

Since,      f = ∇f

After comparing, We get

After observing above equations,

We have,  

Since, , So that,

Thus,  

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(d)

step-by-step explanation:

given: the line in the graph passes through points (5,30) and (6,26).

then, the equation of line is:

now, put y=a(n) and x=n,

hence, option d is correct.