question 4 listen the height of a leaf, h, being carried by the wind is a function of time, t since the…

question 4 listen the height of a leaf, h, being carried by the wind is a function of time, t since the observation began. the graph of the function is shown below. for which interval of time is the leaf moving the fastest? a 3≤t≤4 b 3≤t≤7 c 4≤t≤7 d 1≤t≤3

question 4 listen the height of a leaf, h, being carried by the wind is a function of time, t since the observation began. the graph of the function is shown below. for which interval of time is the leaf moving the fastest? a 3≤t≤4 b 3≤t≤7 c 4≤t≤7 d 1≤t≤3

Answer

Explanation:

Step1: Recall speed - slope relation

The speed of the leaf is related to the slope of the height - time graph. Steeper the graph, faster the leaf is moving.

Step2: Analyze each interval

For interval A ($3\leq t\leq4$): The graph has a steep upward - slope. For interval B ($3\leq t\leq7$): The slope changes from steep upward to less steep downward. For interval C ($4\leq t\leq7$): The slope is less steep downward. For interval D ($1\leq t\leq3$): The slope is relatively less steep.

Step3: Determine the fastest interval

The steepest part of the graph occurs in the interval $3\leq t\leq4$.

Answer:

A. $3\leq t\leq4$