Question

find linearization of the function at the given point
f(x,y) = 1 + ln(xy -5) ; P(2,3)

Answer 1

i need confirmation for the last step. i have f(2,3) = 1; fx(2,3)=6 and fy(2,3)=4.
then plug all into formula to get L(x,y) =6x+4y -23. then? replace (2,3) to get L(2,3)? My confusing is I calculate everything on (2,3) . so the L (x,y) I got must belong to (2,3) why I re-replace (2,3) into the form?

Answer 2

or just stop at linearization form. apply that form at the given point if they ask to get approximation of that point. please, tell me what I should