Stuck on this calculus problem, please help!

Question

f(x,y)=3xy^2-x-y

a) find the equation of the tangent place to the graph of f(x,y) at the point (2,1,3)

b) use the linear approximation to estimate the value of f(2.1,0.9)

c) find the directional derivative of f at (2,1) in the direction of i+j

Answer 1

note that Fx= 3y2-1 = 2 at (2,1) and Fy=6xy-1 = 11 at (2,1) and F(2,1)= 3. Thus the tangent plane will be 2(x-1)+11(y-1)+3 = L(x,y). Note that L(x,y) is also the linear approximation of F nearby (2,1) thus L(2.1,.9)=2.1.

The DD is the del of F. u where u is a unit vector pointing in the desired direction = .707<1,1>. Thus the DD = 2*.707+11*.707= 13/sqrt(2)