A position in options on a particular stock has a delta of zero and a gamma of $4.$ The stock price is $10.$ Which of the following is the approximate relation between the change in the portfolio value in one day, $dP,$ and the return on the stock, $dx$

$dP=2$ times the square of $dx$

$dP=4$ times the square of $dx$

$dP=200$ times the square of

$dP=20$ times the square of $dx$