That is all I have. What kind of information do we need?

#3. (a) (13 points) Let F: R" + R be differentiable at a point a R". Assume F(a) = 0 and VF(a) +0. Let S = {x ER" : F(x)=0}. Using the definition of tangent hyperplane, prove that the hyperplane with normal n = VF(a) through a is a tangent hyperplane of S at a. (b) (12 points) Let S = {(x,y,z) R:+ y2 22 = 1}. Use part (a) to find an equation of a tangent plane of S at point (1, -1, -1). #3. (a) (13 points) Let F: R" + R be differentiable at a point a R". Assume F(a) = 0 and VF(a) +0. Let S = {x ER" : F(x)=0}. Using the definition of tangent hyperplane, prove that the hyperplane with normal n = VF(a) through a is a tangent hyperplane of S at a. (b) (12 points) Let S = {(x,y,z) R:+ y2 22 = 1}. Use part (a) to find an equation of a tangent plane of S at point (1, -1, -1)