Question

a rocket is launched in the air. the graph below shows the height of the rocket h in feet after t seconds. find the interval for which the rockets height is increasing.

Explanation:

Step1: Analyze the graph

The height of the rocket \(h\) is a function of time \(t\). A function \(y = f(x)\) is increasing when, as \(x\) (in this case \(t\)) increases, \(y\) (in this case \(h\)) also increases.

Step2: Determine the interval

Looking at the graph, before \(t = 20\) seconds, as \(t\) increases from \(t=0\) to \(t = 20\), the height \(h\) of the rocket is increasing. After \(t=20\) seconds, as \(t\) increases, the height \(h\) of the rocket is decreasing.

Answer:

The rocket's height is increasing in the interval \(0