1. The height of a bumble bee above the ground is modelled by h(t) = 0.5cos(2π t) + 2, where h is in metres and t

Question

is in seconds. At what time is the bee’s instantaneous rate of change of height with respect to time greatest?
a.) 1 s
b.) 1.25s
c.) 1.5s
d.) 2s

Why is the answer b?
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2. What value for the function y=3cos(t-pi) + 2 gives an instantaneous rate of change of 0?

a) 0
b) pi/2
c) pi/3
d) pi/4

I tried to plug in the options above, but it gave me 4.99999. How do I do this question?
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3. The height of a ball is modelled by the equation h(t)= 4sin(8πt) + 6.5 where h(t) is in metres and t is in seconds. What are the highest and lowest points the ball reaches?

a) 10.5 m and 6.5m
b) 10.5 and 2.5m
c) 6.5m and 2.5m
d) 14.5 and 6.5m

I know that answer won't be B because it has to start at 6.5m

Answer 1

1. The height of a bumble bee above the ground is modelled by h(t) = 0.5cos(2π t) + 2, where h is in metres and t
is in seconds. At what time is the bee’s instantaneous rate of change of height with respect to time greatest?
a.) 1 s
b.) 1.25s
c.) 1.5s
d.) 2s

Why is the answer b?
when is
d/dt 0.5cos(2π t)
biggest?
d/dt = - pi sin(2 pi t)
we want sin(2 pi t) = 1 or -1
that is when 2 pi t = pi/2, 3pi/2, 5 pi/2 , 7 pi/2 ...
t = 1/4 or 3/4 or 5/4 or 7/4 ....
the 5/4 is your 1.25

Answer 2

2.
sin(t-pi) = 0
t = 0, or pi, or 2 pi

perhaps they mean the value of t, not of the function. then t = 0 works

Answer 3

3.
6.5+4 and 6.5-4
10.5 and 2.5

Answer 4

I am still confused for number 2.

For number 3, you used the amplitude(which is 4) to find lowest+highest?