is conservative if we can find a scalar function
such that
. This is equivalent to solving the system of PDEs,
Integrate both sides of the first PDF with respect to :
where is some function independent of
. Then differentiatng with respect to
, we have
and so is indeed conservative, with
Hot Dog Stand
Let
C--------> total cost of the hot dog
x-------> is the number of toppings
we know that
where
The slope of the linear equation is equal to
The y-coordinate of the y-intercept of the linear function is equal to
That means -------> This is the cost of the hot dog without topping
Hamburgers Stand
Let
C--------> total cost of the hamburger
x-------> is the number of toppings
we know that
where
The slope of the linear equation is equal to
The y-coordinate of the y-intercept of the linear function is equal to
That means -------> This is the cost of the hamburger without topping
therefore
<u>the answer is</u>
The linear equation of the hamburger cost is equal to