Chapter 14: Partial Derivatives - Section 14.6 - Tangent Planes and Differentials - Exercises 14.6 - Page 834: 28

a) $3x+4y-6$ b) $0$

a. As we know that $L(x,y)=f(x,y)+f_x(x-m)+f_y(y-n)$ Here, we have $f_x=3$; and $f_y=4$ Thus, we get $L(1,1)=1+3(x-1)+(4)(y-1) \\ \implies L(1,1)=3x+4y-6$ b) As we know that $L(x,y)=f(x,y)+f_x(x-m)+f_y(y-n)$ Here, we have $f_x=0$; and $f_y=0$ Thus, we get $L(0,0)=0+0(x-0)+0(y-0) \\ \implies L(0,0)=0$