Locate the critical point of the function. $f ( x , y ) = 5 x ^ { 2 } + 2 y ^ { 2 } + 4$
A) $( 5,2,137 )$
B) $( 5,2,4 )$
C) $( 0,0,4 )$
D) $( 0,4,4 )$
E) $( 0,0,0 )$

Question

Locate the critical point of the function.   $f ( x , y ) = 5 x ^ { 2 } + 2 y ^ { 2 } + 4$  
A) $( 5,2,137 )$
B) $( 5,2,4 )$
C) $( 0,0,4 )$
D) $( 0,4,4 )$
E) $( 0,0,0 )$

Quizplus · Accepted Answer

To find the critical points of the function $f(x, y) = 5x^2 + 2y^2 + 4$, we need to take the partial derivatives with respect to $x$ and $y$, and set them equal to zero. The partial derivative with respect to $x$ is $10x$, and with respect to $y$ is $4y$. Setting these equal to zero gives $x = 0$ and $y = 0$. Therefore, the critical point is at $(0,0)$. The value of the function at this point is $f(0,0) = 4$, making the correct answer $(0,0,4)$.

Locate the Critical Point of the Function f(x,y)=5x2+2y2+4f ( x , y ) = 5 x ^ { 2 } + 2 y ^ { 2 } + 4f(x,y)=5x2+2y2+4

Locate the Critical Point of the Function $f ( x , y ) = 5 x ^ { 2 } + 2 y ^ { 2 } + 4$