Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. (If the vector field is not conservative, enter DNE.) F(x, y) = (3x2 − 2y2)i + (4xy + 4)j

In this problem, since the condition of equal derivatives does not apply, the vector field is not conservative.

A vector field can be described as:

It is conservative if:

In this problem, the field is:

Then:

Since , the field is not conservative.

A similar problem is given at link

In order for F to be conservative, there must be a scalar function f such that the gradient of f is equal to F. This means

Integrate both sides of the first equation with respect to x :

Differentiate both sides with respect to y :

But we assume g is a function of y, which means its derivative can't possibly contain x, so there is no scalar function f whose gradient is F. Therefore F is not conservative.

$655.61 which is option c

step-by-step explanation:

price of house =   $146,000

initial rate = 3.5%

mortgaged paid in this = 3.5 % of $146,000

                                        =

                                        =$5110

the total years would be = 7

total mortgaged paid = 7 * $5110

                                      =$35770

remaining money = $146000-35770

                                =$110230

new mortgaged payment = 5 % of 110230

                                            =  

                                            =$655.61