Embryo Development The oxygen consumption of a galliform bird embryo increases from the time the chick hatches. In a typical galliform bird the oxygen consumption (in milliliters per hour) can be approximated by c ( t ) = − 0.0027 t 3 + 0.14 t 2 − 0.83 t + 0.15 ( 8 ≤ t ≤ 30 ) , wheret is the time (in days) since the egg was laid. (An egg will typically hatch at around t = 28 .) Use technology to graph c ' ( t ) , and use your graph to answer the following questions. [ HINT: See Example 5.] a. Over the interval [ 8 , 30 ] the derivative c ' is (A) increasing, then decreasing. (B) decreasing, then increasing. (C) decreasing. (D) increasing. b. When, to the nearest day, is the oxygen consumption increasing the fastest? c. When, to the nearest day, is the oxygen consumption increasing at the slowest rate?
Embryo Development The oxygen consumption of a galliform bird embryo increases from the time the chick hatches. In a typical galliform bird the oxygen consumption (in milliliters per hour) can be approximated by c ( t ) = − 0.0027 t 3 + 0.14 t 2 − 0.83 t + 0.15 ( 8 ≤ t ≤ 30 ) , wheret is the time (in days) since the egg was laid. (An egg will typically hatch at around t = 28 .) Use technology to graph c ' ( t ) , and use your graph to answer the following questions. [ HINT: See Example 5.] a. Over the interval [ 8 , 30 ] the derivative c ' is (A) increasing, then decreasing. (B) decreasing, then increasing. (C) decreasing. (D) increasing. b. When, to the nearest day, is the oxygen consumption increasing the fastest? c. When, to the nearest day, is the oxygen consumption increasing at the slowest rate?
Solution Summary: The author explains how to graph the function c(t)=-0.0027t
Embryo Development The oxygen consumption of a galliform bird embryo increases from the time the chick hatches. In a typical galliform bird the oxygen consumption (in milliliters per hour) can be approximated by
c
(
t
)
=
−
0.0027
t
3
+
0.14
t
2
−
0.83
t
+
0.15
(
8
≤
t
≤
30
)
,
wheret is the time (in days) since the egg was laid. (An egg will typically hatch at around
t
=
28
.) Use technology to graph
c
'
(
t
)
, and use your graph to answer the following questions. [HINT: See Example 5.]
a. Over the interval
[
8
,
30
]
the derivative
c
'
is
(A) increasing, then decreasing.
(B) decreasing, then increasing.
(C) decreasing.
(D) increasing.
b. When, to the nearest day, is the oxygen consumption increasing the fastest?
c. When, to the nearest day, is the oxygen consumption increasing at the slowest rate?
Calculus III
May I please have some elaborations on Example 2 part a? Thank you.
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
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Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License