Final answer:
The average rate of change for the function h(t) = cot(t) over the interval [3π/4, 5π/4] is calculated using the average rate of change formula. Both h(3π/4) and h(5π/4) are equal to -1, resulting in a rate of change of 0. Hence, the correct answer is B.
Step-by-step explanation:
The question asks us to calculate the average rate of change of the function h(t) = cot(t) over the interval [3π/4, 5π/4]. To find this, we use the formula for the average rate of change: ∆h/∆t = [h(t_2) - h(t_1)] / [t_2 - t_1]. Here, t_1 = 3π/4 and t_2 = 5π/4.
First, we evaluate h(t) at both ends of the interval:
- h(3π/4) = cot(3π/4) = -1,
- h(5π/4) = cot(5π/4) = -1.
Now, we calculate the rate of change:
∆h/∆t = [-1 - (-1)] / [(5π/4) - (3π/4)] = 0 / (π/2) = 0.
Therefore, the average rate of change of h(t) over the given interval is 0, which corresponds to answer choice B.