91Ó°ÊÓ

Find $f\left(x,y\right)=x+3y$at $\left(0,0\right)$:

$\begin{array}{c}f(0,0)=0+3\left(0\right)\text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰s³Ü²ú²õ³Ù¾±³Ù³Ü³Ù±ð}x=0,y=0\\ =0+0\\ =0\end{array}$

Find $f\left(x,y\right)=x+3y$at $\left(4,0\right)$:

$\begin{array}{c}f(4,0)=4+3\left(0\right)\text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰s³Ü²ú²õ³Ù¾±³Ù³Ü³Ù±ð}x=4,y=0\\ =4+0\\ =4\end{array}$

Find $f\left(x,y\right)=x+3y$at $\left(5,5\right)$:

$\begin{array}{c}f(5,5)=5+3\left(5\right)\text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰s³Ü²ú²õ³Ù¾±³Ù³Ü³Ù±ð}x=5,y=5\\ =5+15\\ =20\end{array}$

Find $f\left(x,y\right)=x+3y$at $\left(0,8\right)$:

$\begin{array}{c}f(0,8)=0+3\left(8\right)\text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰s³Ü²ú²õ³Ù¾±³Ù³Ü³Ù±ð}x=5,y=5\\ =0+24\\ =24\end{array}$

So, the maximum value of $f\left(x,y\right)=x+3y$ is $f\left(0,8\right)=24$and the minimum value of $f\left(x,y\right)=x+3y$is $f\left(0,0\right)=0.$

Here, the maximum value of $f\left(x,y\right)=x+3y$is $f\left(0,8\right)=24$and the minimum value of $f\left(x,y\right)=x+3y$is $f\left(0,0\right)=0.$

The above results match with the option A.

So, the option A is correct.

Here, the maximum value of $f\left(x,y\right)=x+3y$is $f\left(0,8\right)=24$and the minimum value of $f\left(x,y\right)=x+3y$is $f\left(0,0\right)=0.$

The above results do not match with the option B.

So, the option B is incorrect.

Here, themaximum value of $f\left(x,y\right)=x+3y$ is $f\left(0,8\right)=24$and the minimum value of $f\left(x,y\right)=x+3y$is $f\left(0,0\right)=0.$

The above results do not match with the option C.

So, the option C is incorrect.

Here, the maximum value of $f\left(x,y\right)=x+3y$is $f\left(0,8\right)=24$and the minimum value of $f\left(x,y\right)=x+3y$is $f\left(0,0\right)=0.$

The above results do not match with the option D.

So, the option D is incorrect.

The correct option is A, because the maximum value of $f\left(x,y\right)=x+3y$is $f\left(0,8\right)=24$and the minimum value of $f\left(x,y\right)=x+3y$is $f\left(0,0\right)=0.$