Both first partial derivatives of the function $f(x,y)$ are zero at the given points. Use the second$-$derivative test to determine the nature of $f(x,y)$ at each of these points. If the second$-$derivative test is inconclusive, so state.

$f(x,y)=-60x{y}^2+20x^3+2y^4$;$(0,0),(15,15),(15,-15)$

What is the nature of the function at $(0,0)?$

A$.f(x,y)$ has a relative maximum at $(0,0).$

B$.f(x,y)$ has a relative minimum at $(0,0).$

C$.$ The second$-$derivative test is inconclusive at $(0,0).$

D$.f(x,y)$ has neither a relative maximum nor a relative minimum at $(0,0).$