(1 point) Consider the vector field =+4v=yi+4xj and function (,)=422f(x,y)=4x2y2. In this problem we show that the flow lines of the vector field are level curves of the function f.(a) Suppose that ()=()+()r(t)=x(t)i+y(t)j is a flow line of v. Let ()=(())g(t)=f(r(t)). If r is a level curve of (,)f(x,y), that is ()g(t)?()=g(t)=(b) Use the definition of f to find g.(Note that x and y are functions of t, so that your expression should involve factors of x,y,x and y; enter x,y,x and y in your answer rather than ()x(t),()y(t),()x(t) and ()y(t).)=g=(c) Knowing that r is a flow line of the vector field v, what are x and y?=x= =y=(d) Substituting these into your result from (b), what do you get?=g= (Note that this confirms our expectation from (a), showing that the flow lines are level curves of f.)