Let f be a smooth function on Rn, denote by Gf={(x,f(x))∈Rn+1:x∈Rn}. Let g be the restriction of the Euclidean metric on Gf.(1) Prove that g is a complete metric.(2) If there exists Λ>0, such that −ΛIn≤Hess(f)≤ΛIn, where In is the unit matrix of order n, and Hess8f) is the Hessian matrix of f, then the injectivity radius of (Gf,g) is at least 2Λπ. metric spaceinjectivitygeometryanalysiscollege contests