$($Local Max$/$Min$)*$

Consider a function $f(x,y)=3x{e}^y-x^3-e^{3y}.$ How many of the following statements are true?

$($a$)f$ has only one stationary point.

$($b$)-1$ is a local maximum of $f.$

$($c$)f$ has a local maximum at each critical point.

$($d$)f$ has a global maximum at each critical point.

$0$

$1$

$2$

$3$

$4$