need help with math problem asap

Question

1.Find an equation of the tangent plane to the given surface at the specified point.

z = 4x² − y² + 4y, (−2, 4, 16)

my answer was z = -8x-4y but it's incorrect.

2.Find an equation of the tangent plane to the given surface at the specified point.

z = sqrt(xy) at (9,9,9)

thanks

Answer 1

f(x,y,z)=0 is 4x²-y²+4y-z=0

gradient vector = (8x,-2y+4,-1) =(f_x, f_y, f_z)

at (-2,4,16)

grad=(-16,-4,-1) is perpendicular to surface at (-2,4,16)

grad vector dot product [(x+2),(y-4),(z-16)] vector=0

determines plane tangent to surface

16x+4y+z=0

same with (xy)^(1/2)-z=0

grad vector =([y/2][xy]^-1/2,[x/2][xy]^-1/2,-1)

at (9,9,9)

grad=(1/2,1/2,-1)

(1/2,1/2,-1) dot ([x-9],[y-9],z-9])

determines tangent plane vector

x+y-2z=0