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Find all points $(x,y),$ where $f(x,y)$ has a possible relative maximum or minimum. Then use the second$-$derivative test to determine, if possible, the nature of $f(x,y)$ at each of these points. If the second$-$derivative test is inconclusive, so state.

$f(x,y)=2x^2+y^3-x-3y+8$

Using only the first$-$derivative test for functions of two variables, find all the points that are possibly a relative maximum or a relative minimum. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.$ The point$($s$)$ where $f(x,y)$ has a possible relative maximum or minimum is$/$are $(\frac{1}{4},1),(\frac{1}{4},-1{)}^{.}.$

$($Type an ordered pair. Use a comma to separate answers as needed.$)$

B$.$ There is no possible relative maximum or minimum.

Find all of the points $(x,y)$ found earlier at which $f(x,y)$ has a relative minimum. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.$ The relative minimum$/$minima of $f(x,y)$ occur$($s$)$ at $$

$($Type an ordered pair. Use a comma to separate answers as needed.$)$

B$.$ There are no relative minima.