Second 4 O’Clock Exam SolutionsMath 23, Spring 20151.Letf(x, y, z) =x3-2xy+y2+ 2.(a)What is the value of the largest possible directional derivative offat thepoint(1,-1/2)?
(b)Find all the critical points offand determine whether each one is a localmaximum, local minimum, or saddle point.
2.LetSbe the surface determined byx2+ 2y2+z2= 4.(a)Find an equation for the tangent plane toSat the point(-1,1,1).