Question

Challenge: f(x,y)=x^(2)-2y^(2) Find a point (A,B) such that the plane tangent to z=f(x,y) at (A,B,f(A,B)) has an equation 3x+4y+5z=____. Fill in blank.

Answer 1

\[f'(x,y)=2x-4y=0,x=2y\]
\[(A,2A,A^2-2(2A)^2)\rightarrow(A,2A,-7A^2)\]

Answer 2

\[f'(A,B)=2A-4(2A)=-6A\]

Answer 3

\[3x+4y+5z=3(A)+4(2A)+5(-7A^2)=11A-35A^2\]

Answer 4

tried

Answer 5

where did the -7A come from?

Answer 6

in the first step?

Answer 7

nevermind i see now

Answer 8

@UnkleRhaukus ,@cwrw238 ,@Callisto

Answer 9

@Callisto ,@cwrw238