Answer
a) $f(1,1)$ is a local minimum point.
b) $f(1,1)$ is a saddle point.
Work Step by Step
We are given the second partial derivatives $f_{xx}$, $f_{xy}$, and $f_{yy}$. Therefore, using these values, we can calculate D for the Second Derivatives Test to determine if $f(1,1)$ is a local minimum, local maximum, or saddle point.
a) $D=(4)(2)-(1)^2>0$ and $f_{xx}>0$. Therefore, $f(1,1)$ is a local minimum point.
b) $D=(4)(2)-(3)^2<0$. Therefore, $f(1,1)$ is a saddle point.
