Let $f(t)$ be a real-valued function whose second derivative is positive for $-\infty < t < \infty.$ Which of the following statements is/are always true?
- $f(t)$ has at least one local minimum.
- $f(t)$ cannot have two distinct local minima.
- $f(t)$ has at least one local maximum.
- The minimum value of $f(t)$ cannot be negative.