Consider a Continuous Function with the Following Properties $f(0)=3$ $\left|f^{\prime}(x)\right|<0.5$ $f^{\prime \prime}(x)<0$

Multiple Choice

Consider a continuous function with the following properties: $f(0) =3$ $\left|f^{\prime}(x) \right|<0.5$ $f^{\prime \prime}(x) <0$ for $x<0$ $f^{\prime}(1) =0$ . Which of the following are inconsistent with these four conditions?

A) $\lim _{x \rightarrow-\infty} f(x) =0$
B) $f(1) =$ 5
C) $f^{\prime \prime}(1) =0$