frz,y)= 1²-2xy +y? (8,9, 1) Le t 27yty-z =0 Fea,y, z) = ² 21y+y-z
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 27E
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Can you explain to me how it has z variable and how it becomes negative. Does it base on the sign of the point?
The encircle part is the equation
Transcribed Image Text:4:11
Step2
b)
frx, y)= 12- 2xy +y2
(8,9, 1)
Le t
Z- (,y,
27yty- z =0
Fra,y, z) = 1² 214+y-z
Fa Cx, y, z) =
2x - 24
Fy Ca, y, z) =
- 2x+2y
Fz (a,4, z) = -|
Fx (8,9, 1)= 2.8-29 = 16-18 = -2
-2 x8 +2-9 - -16 +18 = 2
Fy (8,9, 1)
Fz C 8,9, 1)
= -|
.. The
equation of the
tangent plane
to
the
Surface
at
(8,9, 1)
is
Fx (8,9,1) (x-8) + Fy (8, 9, 1) CY-9) +F_ (8, 9, 1) (z-1) =0
-2(x-8)+ 2(9-9) -1(2-1) = 0
- 2x+ I6 +2y -18 - z +1 = o
-2x+ 24 -2 -| =0
z= -21 +2y - I
* The equation of the
tangent
Plane
is
Z = -21+ 2y -1
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