Use Lagrange Multipliers to find the maximum value of the function subject to the given constraint. $f\left(x,y,z\right)=e^{x+y+z}:x^{2}+2y^{2}+z^{2}=10$ 1 $10$ $-1b$ es $1$

Question $4$ $4pts$ Use Lagrange multipliers to find the maximum and minimum values of the function below subject to the given constraint. $f\left(x,y\right)=x^{2}y:$ $x^{2}+y^{2}=1$ $O$ O minimum $n=0,$ maximum $num=\dfrac {1} {2\sqrt{2} }$ $O$ O minimum $n=0,$ maximum $num=\dfrac {2} {3\sqrt{3} }$ $\times imum=\dfrac {2} {3\sqrt{3} }$ $○$ minimum $m=-\dfrac {2} {3\sqrt{3} }$ maximum $\times imum=\dfrac {1} {2\sqrt{2} }$ $C$ O minimum $m=-\dfrac {1} {2\sqrt{2} }$ maximum

Use Lagrange Multipliers to find global maximum and minimum values $of:$ $f\left(x,$ $y\right)=x^{2}+2y^{2}-4y$ $\left(1\right)$ subject to the $constraint:$ $x^{2}+y^{2}=9$ $\left(2\right)$