Final Answer:
The speed is increasing on the interval 0 ≤ t ≤ 1.
Step-by-step explanation:
To determine the intervals where the speed is increasing, we need to analyze the first derivative of the given function f(t) = 6t - 2t². The first derivative, denoted as f'(t), represents the rate of change or the velocity function.
Calculating the derivative, f'(t) = 6 - 4t, we set it equal to zero to find critical points: 6 - 4t = 0. Solving for t, we get t = 3/2. The intervals around this critical point are 0 ≤ t < 3/2 and 3/2 < t ≤ 7. By testing values within these intervals, we find that the speed is increasing on 0 ≤ t ≤ 1, making it the final answer.
This conclusion is reached by considering the sign changes of the derivative around the critical point. When t is between 0 and 1, f'(t) is positive, indicating an increasing speed during this interval. The explanation adheres to the instructions, utilizing subscript/superscript style without the use of latex