Answer
See the explanation below.
Work Step by Step
The linearization of $f$ at $(a,b)$ is defined as the linear function and denoted as $L(x,y)$ such as:
$L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)$
and the linear approximation of $f$ at $(a,b)$ is defined as:
$f(x,y) \approx f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)$
Geometrically, it can be interpreted as the tangent plane to the graph of the function $f(x,y)$ at the point $(a,b,f(a,b))$.
