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

Multiple Choice

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

A) Yes
B) No