Question

Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is it minimal? Find the maximal value l1,1,0) aF au - Find two non-collinear unit vectors u, w so that (-1, 1,0- ( Ow 1, 1, 0) = 0 (c) Prove that S defines z as an implicit functionz fir, y) near the point p1,0). Find the partial derivatives f f(-1,1) (d) Find the directional derivative , -1,1) of () in the direction of the unit vector v-(vi , U2) at the point (-1,1 -In what direction u is this derivative maximal? Find the maximal value |--(-1.11 -Find a unit vector u such that (-1,1) 0 of

Answer 1

(x,y,2), 2 ro be 4k poAi teen ト。Sİhso n veckrづ.ry うメ Z. 2. 을 一.qee 2 ーマた

Scalar df le f 37cq + (2,2.ty)て 十 92 min valuu
I don't understand what is f.