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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Topic Video
Question
I need help answering 19.
![Problems
(T/2, 1)
1
In Exercises 6–7, identify each of the marked points as being an
absolute maximum or minimum, a relative maximum or mini-
mum, or none of the above. (A point could be more than one.)
-1
(37/2, -1)
6.
12. fx) — х?V4 —х
y
4
6
(부, )
10
B
RD
(4,0)
7.
(0,0)
2
4
Sx x<0
x x> 0
13. f(x) =
8.
(a) Sketch the graph of a function that has a local mini-
1
mum at 3 and is differentiable at 3.
(b) Sketch the graph of a function that has a local mini-
0.5
mum at 3 and is continuous but not differentiable at
3.
(c) Sketch the graph of a function that has a local mini-
-0,5
(0, 0) 0,5
mum at 3 and is not continuous at 3.
-0,5
In Exercises 9-15, evaluate f'(x) at the points indicated in the
graph.
(x x<0
14. f(x) =
9. f(x)
x> 0
x2 + 1
y
1-
(0, 2)
0,5
-1
-0,5
(0, 0) 0,5
-0.5
150
(x – 2)2/3
+1
In x
24. f(x) =
[1, 4).
15. f(x) =
on
25. f(x) = x13 - x
(0, 2].
on
26. Show that 4 is a critical number of f(x) = (x – 4) +7 but
f does not have a relative extreme value at 4.
27. A cubic function is a polynomial of degree 3; that is, it has
the form ax + bx? + cx + d, where a + 0.
(6,1+ )
2
(2, 1)
(a) Show that a cubic function can have 2, 1, or 0 critical
numbers. Give examples and sketches to illustrate
the 3 possibilities.
10
In Exercises 16–25, find the extreme values of the function on
the given interval.
(b) How many local extreme values can a cubic function
have?
16. f(x) = x + x + 4 on
(-1, 2).
9.
17. f(x) — х -
28. Suppose that a and b are positive numbers. Find the ex-
treme values of f(x) = x° (1 – x)° on [0, 1).
30х + 3 on
(0, 6).
18. f(x) = 3 sin x on
[T/4, 27/3).
Review
19. f(x) — х*V4 — х? on
[-2, 2).
3
on
dy
where x'y – yx = 1.
dx'
20. f(x) = x +
[1, 5].
29. Find
30. Find the equation of the line tangent to the graph of x +
y + xy = 7 at the point (1, 2).
21. f(x) =
[-3, 5).
on
x² + 5
22. f(x) — е' сos x
[0, 1].
31. Let f(x) = x³ + x.
on
f(x+s) – f(x)
23. f(x) = e* sin x
[0, 7].
Evaluate lim
on](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf266520-407e-4b51-839c-e1d92d759be6%2F10e9725d-a818-45f2-b5d4-835592e1d81e%2F9opuq6h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problems
(T/2, 1)
1
In Exercises 6–7, identify each of the marked points as being an
absolute maximum or minimum, a relative maximum or mini-
mum, or none of the above. (A point could be more than one.)
-1
(37/2, -1)
6.
12. fx) — х?V4 —х
y
4
6
(부, )
10
B
RD
(4,0)
7.
(0,0)
2
4
Sx x<0
x x> 0
13. f(x) =
8.
(a) Sketch the graph of a function that has a local mini-
1
mum at 3 and is differentiable at 3.
(b) Sketch the graph of a function that has a local mini-
0.5
mum at 3 and is continuous but not differentiable at
3.
(c) Sketch the graph of a function that has a local mini-
-0,5
(0, 0) 0,5
mum at 3 and is not continuous at 3.
-0,5
In Exercises 9-15, evaluate f'(x) at the points indicated in the
graph.
(x x<0
14. f(x) =
9. f(x)
x> 0
x2 + 1
y
1-
(0, 2)
0,5
-1
-0,5
(0, 0) 0,5
-0.5
150
(x – 2)2/3
+1
In x
24. f(x) =
[1, 4).
15. f(x) =
on
25. f(x) = x13 - x
(0, 2].
on
26. Show that 4 is a critical number of f(x) = (x – 4) +7 but
f does not have a relative extreme value at 4.
27. A cubic function is a polynomial of degree 3; that is, it has
the form ax + bx? + cx + d, where a + 0.
(6,1+ )
2
(2, 1)
(a) Show that a cubic function can have 2, 1, or 0 critical
numbers. Give examples and sketches to illustrate
the 3 possibilities.
10
In Exercises 16–25, find the extreme values of the function on
the given interval.
(b) How many local extreme values can a cubic function
have?
16. f(x) = x + x + 4 on
(-1, 2).
9.
17. f(x) — х -
28. Suppose that a and b are positive numbers. Find the ex-
treme values of f(x) = x° (1 – x)° on [0, 1).
30х + 3 on
(0, 6).
18. f(x) = 3 sin x on
[T/4, 27/3).
Review
19. f(x) — х*V4 — х? on
[-2, 2).
3
on
dy
where x'y – yx = 1.
dx'
20. f(x) = x +
[1, 5].
29. Find
30. Find the equation of the line tangent to the graph of x +
y + xy = 7 at the point (1, 2).
21. f(x) =
[-3, 5).
on
x² + 5
22. f(x) — е' сos x
[0, 1].
31. Let f(x) = x³ + x.
on
f(x+s) – f(x)
23. f(x) = e* sin x
[0, 7].
Evaluate lim
on
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