Let f : R" -> R be a twice differentiable function with a positive semidefinite hessian. For any two points r, y ( R", we will show that the one-dimensional function g : [0, 1] -+ R defined as g(t) := f(tx + (1 -t)y) is convex. (i) Compute g'(t) and g" (t), and show that g" (t) 2 0. (ii) Using Taylor's theorem prove that g(0) > g(t) + g'(t)(-t) g(1) 2 g(t) + g'(t) (1 - t) (iii) From part (ii), conclude that g is convex