Let f(x,y,z) =x+y+z, let B be a ball of radius 1 around the origin,and let S be its surface a). Compute the gradient of f b) Explain why f does not have any extreme points in the interior of B. c) Come up with a function g(x,y,z) such that S can be described as a set of points where g(x,y,z) is equal to some constant d) Use Lagrange multipliers to find the extreme points of f over S e) Use the direction of the gradient in order to decide which of those extreme points is the maximum of f over B, and which is the minimum.

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