Answer
$$z = {f_x}\left( {x,y} \right)\left( {x - a} \right) + {f_y}\left( {x - b} \right) + f\left( {a,b} \right)$$
Work Step by Step
$$\eqalign{
& {\text{ }}z = f\left( {x,y} \right) \cr
& {\text{Let }}f\left( {x,y} \right){\text{ differentiable at the point }}\left( {a,b} \right).{\text{ An equation of the}} \cr
& {\text{plane tangent to the surface }}z = f\left( {x,y} \right){\text{ at the point}} \cr
& \left( {a,b,f\left( {a,b} \right)} \right){\text{ is:}} \cr
& z = {f_x}\left( {x,y} \right)\left( {x - a} \right) + {f_y}\left( {x - b} \right) + f\left( {a,b} \right) \cr} $$
