MATH 2321 Lecture 19: 2.7 cont

• School: Northeastern University
• Department: Mathematics
• Course: MATH 2321
• Professor: Sumi Seo

Document Summary

C) find parametric equations for the normal line to the level cune x,y)= 1 at p=(1,-1). Mi z = 3x2 - y +2x = f(x, y, z)= 3x2-y{+ 2x-z=0: find egn. For tangent plane to the surface at point (1;-2,1) Fx (1,-2, 1)(x-1) + fy (1,-2,1) (x+2) +ez (1, 2,1) (2-1)= 0 :: Ef = (fx, fy, ez) = (6x+2;-29, -1). For the line which passes through point (1,-2 ;)) and is normal to the surface m at (1,2,1). (x, y, z)=(1,-2,1)++(8,4, -1) F:r" sr ip is a critical point of f iff ff(p) = 0 or if is not differentiable at point ipi. X?_y? i: critical points: fg = (gx, gy, gz) = (-2x,-2y; 27-2)=(0,0,0). x=0, x=0, z= 1 (0,0,1) G(0,0, 1) = -1 sketch graph of level surface, where g=-| For tangent plane to the level surface of g at : 13,4,6) Fg(3,4,6). (x-3,4-4,2-6) = 0 (-28, -24, 27-2)) : (x-3.