32. In Example 4 of Section 1.2, we examined how CO2 concentrations (in ppm) have varied from 1974 to 1985. Using linear and periodic functions, we found that the following function gives an excellent fit to the data: f(x) = 0.122463x + 329.253 + 3 cos () ppm where x is months after April 1974. Using the closed interval method, find the global maximum and mini- mum CO2 levels on the interval [12, 24].
32. In Example 4 of Section 1.2, we examined how CO2 concentrations (in ppm) have varied from 1974 to 1985. Using linear and periodic functions, we found that the following function gives an excellent fit to the data: f(x) = 0.122463x + 329.253 + 3 cos () ppm where x is months after April 1974. Using the closed interval method, find the global maximum and mini- mum CO2 levels on the interval [12, 24].
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question 32
![298 Chapter 4 Applications of Differentiation
In Problems 5 to 12, find the critical points and use the
first derivative test to classify them.
1
on [-1, )
X + 2
29. f(x) — х +
30. f(x) — хе* on (-, —1]
5. y = 1+3x +4x²
6. f (x) — 10 + 6х — х2
3x4
+5
4
Level 2 APPLIED AND THEORY PROBLEMS
7. f(t) = t?e-
8. y = x³
31. Let f be defined on (a, b) and c e (a, b). Prove that
if x = c is a local maximum and f is differentiable at
x = c, then f'(c)= 0.
32. In Example 4 of Section 1.2, we examined how CO2
concentrations (in ppm) have varied from 1974 to
1985. Using linear and periodic functions, we found
that the following function gives an excellent fit to
+3
9. f(x) =
10. у — — 3х— х2 +
3
-
1+ x
3x2
x3
11. y = -x +
4
12. y = et²-21+1
3
the data:
In Problems 13 to 16, find the critical points and use the
second derivative test to classify them.
IT X
f(x) = 0.122463x + 329.253 + 3 cos
ppm
6.
9 x²
where x is months after April 1974. Using the closed
interval method, find the global maximum and mini-
mum CO2 levels on the interval [12, 24].
33. In the previous problem, use the closed interval
method and find the global maximum and minimum
CO2 levels between April 2000 and April 2001.
34. A close relative of the codling moth is the pea moth,
Cydia nigricana, which is a pest of cultivated and
garden peas in several European countries. If its
search period in one of the regions where it is a pest
is given by the function
13. у — — 12 х
+x3 14. у %3D 1 - еxp(-x?)
2
2.x2 – x4
1
15. у %%3D х +
16. у
2+ x
4
In Problems 17 to 20, use the closed interval method to
find the global extrema on the indicated intervals.
17. f(x) — х? — 4х + 2 on [0, 3]
18. f(x) — х3 - 12х + 2 on[-3, 3]
1
19. f(x) = x +- on [0.1, 10]
1
s(T)
for 20 < T < 30,
X
-0.04T2 +2T – 15
20. f(x)= xe-* on [0, 100]
then graph s(T) using information about the first
derivative over the domain 20 < T < 30. Be sure
that your graph indicates the largest and smallest
In Problems 21 to 24, use the open interval method to](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4db1e84-75df-498d-9686-5cabfd0e0c2f%2F86763465-5568-49af-a647-37ddc699b227%2Fxvbrgrx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:298 Chapter 4 Applications of Differentiation
In Problems 5 to 12, find the critical points and use the
first derivative test to classify them.
1
on [-1, )
X + 2
29. f(x) — х +
30. f(x) — хе* on (-, —1]
5. y = 1+3x +4x²
6. f (x) — 10 + 6х — х2
3x4
+5
4
Level 2 APPLIED AND THEORY PROBLEMS
7. f(t) = t?e-
8. y = x³
31. Let f be defined on (a, b) and c e (a, b). Prove that
if x = c is a local maximum and f is differentiable at
x = c, then f'(c)= 0.
32. In Example 4 of Section 1.2, we examined how CO2
concentrations (in ppm) have varied from 1974 to
1985. Using linear and periodic functions, we found
that the following function gives an excellent fit to
+3
9. f(x) =
10. у — — 3х— х2 +
3
-
1+ x
3x2
x3
11. y = -x +
4
12. y = et²-21+1
3
the data:
In Problems 13 to 16, find the critical points and use the
second derivative test to classify them.
IT X
f(x) = 0.122463x + 329.253 + 3 cos
ppm
6.
9 x²
where x is months after April 1974. Using the closed
interval method, find the global maximum and mini-
mum CO2 levels on the interval [12, 24].
33. In the previous problem, use the closed interval
method and find the global maximum and minimum
CO2 levels between April 2000 and April 2001.
34. A close relative of the codling moth is the pea moth,
Cydia nigricana, which is a pest of cultivated and
garden peas in several European countries. If its
search period in one of the regions where it is a pest
is given by the function
13. у — — 12 х
+x3 14. у %3D 1 - еxp(-x?)
2
2.x2 – x4
1
15. у %%3D х +
16. у
2+ x
4
In Problems 17 to 20, use the closed interval method to
find the global extrema on the indicated intervals.
17. f(x) — х? — 4х + 2 on [0, 3]
18. f(x) — х3 - 12х + 2 on[-3, 3]
1
19. f(x) = x +- on [0.1, 10]
1
s(T)
for 20 < T < 30,
X
-0.04T2 +2T – 15
20. f(x)= xe-* on [0, 100]
then graph s(T) using information about the first
derivative over the domain 20 < T < 30. Be sure
that your graph indicates the largest and smallest
In Problems 21 to 24, use the open interval method to
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