At what point is the following function a local minimum? $f ( x , y ) = 8 x ^ { 2 } + 5 y ^ { 2 }$
A) $( 5,0 )$
B) $( 8 , - 5 )$
C) $( 8,0 )$
D) $( 8,5 )$
E) $( 0,0 )$

Question

Quizplus · Accepted Answer

The function $f(x, y) = 8x^2 + 5y^2$ is a quadratic form, which is minimized at the origin $(0,0)$ since both coefficients of $x^2$ and $y^2$ are positive, indicating a paraboloid opening upwards.

At What Point Is the Following Function a Local Minimum f(x,y)=8x2+5y2f ( x , y ) = 8 x ^ { 2 } + 5 y ^ { 2 }f(x,y)=8x2+5y2

At What Point Is the Following Function a Local Minimum $f ( x , y ) = 8 x ^ { 2 } + 5 y ^ { 2 }$