1. which of the following is the correct formula to be used in the second derivatives test?(single…

1. which of the following is the correct formula to be used in the second derivatives test?(single choice)*\nd=(f_xy)(f_yx)-(f_xx)^2\nd=(f_xy)(f_xx)-(f_yy)^2\nd=(f_xy)(f_yy)-(f_xx)^2\nd=(f_xx)(f_yy)-(f_xy)^2

1. which of the following is the correct formula to be used in the second derivatives test?(single choice)*\nd=(f_xy)(f_yx)-(f_xx)^2\nd=(f_xy)(f_xx)-(f_yy)^2\nd=(f_xy)(f_yy)-(f_xx)^2\nd=(f_xx)(f_yy)-(f_xy)^2

Answer

Brief Explanations:

In the Second - Derivatives Test for a function of two variables $z = f(x,y)$, the discriminant $D$ is defined as $D = f_{xx}f_{yy}-(f_{xy})^2$, where $f_{xx}=\frac{\partial^{2}f}{\partial x^{2}}$, $f_{yy}=\frac{\partial^{2}f}{\partial y^{2}}$ and $f_{xy}=\frac{\partial^{2}f}{\partial x\partial y}$.

Answer:

D. $D=(f_{xx})(f_{yy})-(f_{xy})^2$