Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 6z) k C is the line segment from (2, 0, −2) to (5, 4, 2) (a) Find a function f such that F = ∇f. f(x, y, z) = Correct: Your answer is correct. (b) Use part (a) to evaluate C ∇f · dr along the given curve C.

Required solution (a) (b) 40.

Step-by-step explanation:

Given,

(a) Let,

Then,

Integrating we get,

Differentiate this with respect to y we get,

compairinfg with of the given function we get,

Then,

Again differentiate with respect to z we get,

on compairing we get,

  (By integrating h'(z))  where C is integration constant. Hence,

(b) Next, to find the itegration,

this was already solved by me with a different person. if you look it up in the search bar at the top of the page, you will get the answer.

step-by-step explanation:

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.