Question

Lesson 12.B

1.Over what interval does 3 cos(2?) have the greatest positive rate of change?

a) [0.8, 1.0]

b) [1.2, 1.4]

c) [2.2, 2.4]

d) [2.8, 3.0]

2. Let ?(?) = 2 cos(?) and ?(?) = cos(2?). Consider the average rate of change of these functions over intervals of length 0.1. •

Define ?? to be the maximum such rate of change for the function ? for 0 ≤ ? ≤ 2?. •

Define ?? to be the maximum such rate of change for the function ? for 0 ≤ ? ≤ 2?.

Which is greater, ?? or ??? Or are they the same? 9

3. Let ?(?) = 2 cos(?) and ?(?) = sin(3?). Consider the average rate of change of these functions over intervals of length 0.1. •

Define ?? to be the maximum such rate of change for the function ? for 0 ≤ ? ≤ 2?. • Define ?? to be the maximum such rate of change for the function ? for 0 ≤ ? ≤ 2?.

Which is greater, ?? or ??? Or are they the same?

Lesson 12.C

1. The electric current in an electric circuit oscillates according to the function

?(?) = 3? −0.5? sin(2? − 0.5)

where current is measured in amps and time is measured in seconds. Use a graph to estimate the time when the current is at a maximum.

a) 0.9 sec

b) 1.4 sec

c) 3.0 sec

d) 4.6 sec

2. The electric current in a circuit oscillates according to the function

?(?) = 3? −0.5? sin (2t − 0.5)

where current is measured in amps and time is measured in seconds. Use a graph to estimate the maximum current.

a) – 0.1 amps

b) – 1.4 amps

c) 1.8 amps

d) 0.4 amps

Answer 1