Suppose that the function $f ( x , y )$ and the linear function $L ( x , y ) = 4 - 3 x + 5 y$ satisfy $| f ( x , y ) - L ( x , y ) | \leq 5 \left( x ^ { 2 } + y ^ { 2 } \right)$ for points $( x , y )$ close to $( 0,0 )$ .Find $f _ { x } ( 0,0 )$ and $f _ { y } ( 0,0 )$ .

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The Answer of Suppose that the function $f ( x , y )$ and the linear function $L ( x , y ) = 4 - 3 x + 5 y$ satisfy $| f ( x , y ) - L ( x , y ) | \leq 5 \left( x ^ { 2 } + y ^ { 2 } \right)$ for points $( x , y )$ close to $( 0,0 )$ .Find $f _ { x } ( 0,0 )$ and $f _ { y } ( 0,0 )$ .

Suppose That the Function f(x,y)f ( x , y )f(x,y) And the Linear Function

Suppose That the Function $f ( x , y )$ And the Linear Function