Question

Please do the parts in the given order

tyā (x,y)メ(0,0) (x,y)= (0,0). if if 1 (d) Given the unit vector u-( find the directional derivative of f(x, y) at the 리지, ,- point (to,m) = (0,0), in the direction of the vector a. (e) Find the gradient of f(x, y) at the point (zo,o) (0,0) (c) Find the equation of the tangent plane to the graph of the function z -f(x, y) at the point (x,y,z) (1,0,0).

Answer 1

f, (0,0) = lim ,f( 0 +1,0)-f(0,0)=limfih,0)'f( 0,0 )=1 0-0 =0 0.0)= lim-f( 0,0 + k)-f(0,0)=lim 0-0-0 So the directional derivative of f(x, y) at (0,0) in the direction of u is (0,0)=儀(0,0)./ (0,0))is(0,0)に1)-0 Gradient off(xy_Vr 0,0)= (0.0) f, (0,0)) =(0,0) ( c ) Differentiate/( x, y) = partially to get RAFT → (1,0,0)=111-01-1 So the equation of the tangent plane at (1,0,0) is --0- (1,0,0)(x-1)+养(1,0,0)(y-0) =0(x-1)+1(y-0)