Answer
a) $-x+2y+1$ b) $-e^3+2e^3y-2e^3$
Work Step by Step
Since, we have $L(x,y)=z_0+f_x(x-a)+f_y(y-b)$ ...(1)
a ) Now,
$f_x=-1$; and $f_y=2$
Now eq. (1) becomes $L(0,0)=1+(-1)(x-0)+2(y-0)=-x+2y+1$
b) Since, we have $L(x,y)=z_0+f_x(x-a)+f_y(y-b)$ ...(1)
Now,
$f_x=-e^3$; and $f_y=2e^3$
Now eq. (1) becomes $L(1,2)=e^3-e^3(x-1)+2e^3(y-2)
=-e^3+2e^3y-2e^3$
Hence, a) $-x+2y+1$ b) $-e^3+2e^3y-2e^3$
