Locate and classify all critical points for the given function.
-$f(x, y)=x^{2}+x+y^{2}-y-5$
A) Minimum of $-\frac{7}{2}$ at $\left(-\frac{1}{2},-\frac{1}{2}\right)$
B) Maximum of $-\frac{7}{2}$ at $\left(-\frac{1}{2},-\frac{1}{2}\right)$
C) Minimum of $-\frac{7}{2}$ at $\left(-\frac{1}{2}, \frac{1}{2}\right)$
D) Maximum of $-\frac{7}{2}$ at $\left(-\frac{1}{2}, \frac{1}{2}\right)$

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The Answer of Locate and classify all critical points for the given function.
-$f(x, y)=x^{2}+x+y^{2}-y-5$
A) Minimum of $-\frac{7}{2}$ at $\left(-\frac{1}{2},-\frac{1}{2}\right)$
B) Maximum of $-\frac{7}{2}$ at $\left(-\frac{1}{2},-\frac{1}{2}\right)$
C) Minimum of $-\frac{7}{2}$ at $\left(-\frac{1}{2}, \frac{1}{2}\right)$
D) Maximum of $-\frac{7}{2}$ at $\left(-\frac{1}{2}, \frac{1}{2}\right)$

Locate and Classify All Critical Points for the Given Function f(x,y)=x2+x+y2−y−5f(x, y)=x^{2}+x+y^{2}-y-5f(x,y)=x2+x+y2−y−5

Locate and Classify All Critical Points for the Given Function $f(x, y)=x^{2}+x+y^{2}-y-5$