Find an equation of the tangent plane to the given surface at the specified point. z=2(x-1)^2+6(y+3)^2+4,\ (3,-2,18)

DofotheroU

DofotheroU

Answered question

2021-05-18

Find an equation of the tangent plane to the given surface at the specified point.
z=2(x1)2+6(y+3)2+4, (3,2,18)

Answer & Explanation

smallq9

smallq9

Skilled2021-05-19Added 106 answers

Find an equation of the tangent plane to the given surface at the specified point.
z=2(x1)2+6(y+3)2+4,(3,2,18)
zx=4(x1)
=4x4,
zy=12(y+3)
=12y+36
At the point (3,-2,18):
zx=4x4
=4(3)4
=124
=8
zy=12y+36
=12(2)+36
=24+36
=12
Equation of the tangent plane is,
zz1=zx(xx1)+zy(yy1)
z18=8(x3)+12(y(2))
z18=8x+12y
z=8x+12y+18

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