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The graph shows the height \( h \) of a rocket over time \( t \), and you are asked to find the interval during which the rocket's height is increasing.

In this case, the rocket's height is increasing when the graph is rising. This occurs from \( t = 0 \) to the point where the graph reaches its maximum height at \( t = 20 \) seconds. 

Thus, the interval for which the rocket's height is increasing is:
\[
0 \leq t \leq 20 \text{ seconds}.
\]

Would you like any further explanation or have any questions about this? Here are five related questions to expand on the topic:

1. How can you find the interval where the rocket's height is decreasing?
2. How do you find the maximum height of the rocket from the graph?
3. What mathematical concept explains why the height increases then decreases?
4. How can you use derivatives to find increasing and decreasing intervals of a function?
5. How would the interval change if the rocket took more time to reach its maximum height?

**Tip:** Always look for the highest and lowest points on a graph to determine increasing and decreasing intervals.

A rocket is launched in the air. The graph shows the height of the rocket h in feet after t seconds. Find the interval for which the rocket's height is increasing.

Explore how to determine the interval in which a rocket's height is increasing based on a graph. This problem focuses on the interpretation of parabolic graphs and finding the point at which the height reaches its maximum.

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