Which of the following is true for every function $u: \mathbb{R} \rightarrow \mathbb{R}$ which is continuously differentiable on $\mathbb{R} \;\text{(i.e}., u$ is diffferentiable on $\mathbb{R}$ and its derivative $u^{\prime}$ is continuous on $\mathbb{R})$, and satisfies
\[ u(y) \geq u(x)+u^{\prime}(x)(y-x) \] for all $x, y \in \mathbb{R}?$
- $u^{\prime}$ is nonnegative.
- $u$ attains a minimum at some $x \in \mathbb{R}$.
- $u^{\prime}$ is nondecreasing.
- $u^{\prime}$ is nonincreasing.
