Question

1) Assume you are given the surface S with equation 2 1- (a) Find the equation of the tangent plane to S at the point (V6, 1) (b) Find a point on the surface S so that the tangent plane to S at that point contains the point (3,0, 0). (c) Give an equation for and geometrically describe the set of points on S so that the tangent plane to S at those points contains the point (3, 0,0).

Answer 1

olofion ariven Surfas atep + Ca) Carivew (oint ( ) & r y2 C2) ln egeual on of taugour flans to RoN-fac at 0 (x-Xo) 1,1547 ( JB, plaw t (aueur Clu (3-1)- -1, 15u7) (-)-oF) Y- C 3, 0,0) The d'slana bron Co) noint (1,4, 3) pt (3,0,0) d. u-3 2 Bot (4,)ke on 4

2 y-un2 ++ , 2 - 31 t +12 ) :0 fyco Tharve bre Cret Cal fcint Co, 0) gecond deriv alue lak fuy 9-2 KLG lnoww y Ca,6) f G.6)- 0 = CO naint i&:(3, 0, J2) tHenu AMbme e Cet od noinG need at (9,&)-(00) 42 f X up dy -y C 23 t uldn)

a Co,o) 0 Qn d 04 (auyent plan approrinaloni e 1441, &t4)f(y)) Ay F l0,0) (t C0)f (0) J(tAy