AB CALCULUS – 5.4/5.5 WORKSHEET 2.0
Name ________________
Calculator Active Question
Let 𝑓(𝑥) be a function that is differentiable on [0, 2𝜋] and let 𝑓 + 𝑥 = − cos 𝑥. If 𝑓 0 = −5, find
.
the 𝑥-coordinate of the absolute minimum value of 𝑓(𝑥) on [0, 2𝜋]. Justify your answer
What would be your guess as to the 𝑥-coordinate of the absolute maximum value of 𝑓(𝑥) on
[0, 2𝜋]?
Calculator-Active Rectilinear Motion Question
A particle is moving on a horizontal axis with its velocity in meters per second given by
9
𝑣(𝑡) = 5 tan
− 5 for 0 ≤ 𝑡 ≤ 10 seconds.
:
a) At what time is the particle stopped?
b) For what times is the particle’s velocity increasing?
c) For what times is the particle’s velocity decreasing?
d) For what times is the particle speeding up?
e) For what times is the particle slowing down?
f) At what time is the particle farthest to the left?
g) What are the absolute maximum and minimum values for the velocity of the particle?
h) What is the acceleration of the particle when t = 9.5?
i) What is the average acceleration on the interval 𝑡 ∈ [0,10]
j) For what value of time is the instantaneous acceleration equal to the average acceleration?