Question

6. The point(0,0) in the domain of f(x, y)=sin(x) is a point of
a) Saddle
bNunima
c) Maxima
d) Constant​

Answer 1

The point $(0,0)$ in the domain of $f(x,y)=sinx$. (option d).

• Find the first derivative of the function with respect to x and y.

$f_{x}=cosx\\f_{y}=0$

• Find the second derivative of the function with respect to x and y.

$f_{xx}=-sinx\\f_{yy}=0$

• Find the derivative of $f_x$ with respect to y.

$f_{xy}=0$

• Find $f_{xx}\cdot f_{yy}-f_{xy}$.

$-sinx\cdot0-0=0$

• Since $f_{xx}\cdot f_{yy}-f_{xy}=0$ that means no conclusion is drawn. So, option (d) is correct.