Let

f(x)=x^(T)Ax+2b^(T)x+c

, where

AinR^(n\\\\times n)

is symmetric,

binR^(n)

, and

cinR

.\ Suppose that

A>-=0

. Show that

f

is bounded below

^(1)

over

R^(n)

if and only if

bin

\

Range(A)={():}

Ay

{::yinR^(n)}

.

Let f(x)=xTAx+2bTx+c, where ARnn is symmetric, bRn, and cR. Suppose that A0. Show that f is bounded below 1 over Rn if and only if b Range(A)={ Ay :yRn}