A.

For all $x ＞ 0$ , it is true that $2^{x} < x^{2} + 1$ .

B.

For all $x ＞ 0$ , it is true that $2^{x} ＞ x^{2} + 1$ .

C.

There are constants $c_{1}$ and $c_{2}$ such that if $0 < x < c_{1}$ , then $2^{x} ＞ x^{2} + 1$ , but if $c_{1} < x < c_{2}$ , then $2^{x} < x^{2} + 1$ , and if $x ＞ c_{2}$ , then $2^{x} ＞ x^{2} + 1$ .

D.

There are constants $c_{1}$ and $c_{2}$ such that if $0 < x < c_{1}$ , then $2^{x} < x^{2} + 1$ , but if $c_{1} < x < c_{2}$ , then $2^{x} ＞ x^{2} + 1$ , and if $x ＞ c_{2}$ , then $2^{x} < x^{2} + 1$ .