Suppose That There Exists a Linear Function $L ( x , y )$

True/False

Suppose that there exists a linear function $L ( x , y )$ near the point (0,0)such that the difference between $f ( x , y )$ and $L ( x , y )$ approaches 0 as $( x , y )$ approaches (0,0).Then f is differentiable at (0,0)with $L ( x , y )$ as its local linearization.