1. **State the problem:** We have a function $h(s)$ representing the height above sea level of a road at position $s$ miles, with domain $[0,10]$. The function has a single critical point at $s=6$. The derivative $h'(s)$ is negative on $[0,6)$ and positive on $(6,10]$. We need to determine the nature of the critical point at $s=6$. 2. **Recall the first derivative test:** If $h'(s)$ changes from negative to positive at a critical point $s=c$, then $h(c)$ is a local minimum. 3. **Analyze the given derivative behavior:** Since $h'(s)<0$ for $s<6$ and $h'(s)>0$ for $s>6$, the slope changes from decreasing to increasing at $s=6$. 4. **Conclusion about the critical point:** By the first derivative test, $h(6)$ is a local minimum. 5. **Determine if it is absolute:** Since the function is defined on a closed interval $[0,10]$ and $s=6$ is the only critical point, and the derivative changes from negative to positive, the function decreases before $6$ and increases after $6$. This means $h(6)$ is the lowest point on the interval, so it is an absolute minimum. **Final answer:** The elevation above sea level reaches an absolute minimum at $s=6$.