Chapter 13.7, Problem 21ES

Determine whether the statement is true or false. Explain your answer.

If the tangent plane to the graph of $z=f\left(x,y\right)$ at the point $\left(1,2,1\right)$ has equation $2x+y-z=3,$ then the local linear approximation to $f\text{at}\left(1,2\right)$ is given by the function $L\left(x,y\right)=1+2\left(x-1\right)+\left(y-2\right).$