The keyword here is MUST.

A. $x+1$. This need not be negative. If x = -0.1, then x + 1 = -0.1 + 1 = 0.9 (which is positive). ELIMINATE

B. $-x+1$. If x = -1, then -x + 1 = -(-1) + 1 = 1 + 1 = 2 (which is positive). ELIMINATE

C. $x^{-1} = \frac{1}{x}= \frac{1}{negative}= negative$. KEEP

D. $x^{3}$. ODD powers PRESERVE the sign of the base. Since the base (x) is NEGATIVE, and since 3 is ODD, we know that $x^{3}$ must be negative. KEEP

E. $-5x$. If x = -1, then -5x = -5(-1) = 5 (which is positive). ELIMINATE

F. $x^{2}$. If x = -1, then $x^{2} = (-1)^{2} = (-1)(-1) = 1$ (which is positive). ELIMINATE

Answer: C, D

Cheers,
Brent