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
Q19,21,23,29&Q31
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Must solve all mentioned above
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![EXERCISES 3.1
Differentiate the functions in Exercises 1-28.
1. y= (x+1)(x3 +5x+2) 2. y = (-x³ +
3. y = (2x4x + 1)(-x³ + 1) 4. y = (x² + x + 1)³(x - 1)4
5. y = x(x² + 1)4
6. y=x√x
7. y = (x²+3)(x²-3) 10
8. y=[(-2x³ + x)(6x -
9. y= (5x+1)(x2 − 1) +
10. y = x²(3x4 + 12x - 1)²
x-1
11. y=
x+1
13. y =
15. y=
17. y =
19. y =
22. y=
23. y=
x² - 1
x² +1
x+3
(2x + 1)²
25. y =
1
TT
+
2
x² + 1
y=(x+11)'
x²
(x² + 1)²
21. y = [(3x² + 2x + 2)(x-2)]²
1
√x-2
1
Vx+1
2x + 1
3
27. y = √x + 2(2x + 1)²
12. y =
14. y =
X
x +
16. y=x² + 4x
18. y=
20. y =
24. y =
26. y =
+ 2)( ½ − 1)
28. y=
1
x²+x+7
ax + b
cx + d
(x + 1)³
(x - 5)²
3
√√x+1
x+3
x² + 1
√3x - 1
x
-3)]4
29. Find the equation of the tangent line to the curve
y = (x-2)(x + 1)² at the point (3, 16).
30. Find the equation of the tangent line to the curve
y = (x + 1)/(x - 1) at the point (2, 3).
31. Find all x-coordinates of points (x, y) on the curve
y = (x-2)/(x-4)³ where the tangent line is horizontal.
32. Find the inflection points on the graph of y=-
Fig. 2.)
Figure 2
33. Find all x such that
dy
dx
1
Y
y =
= 0, where
1
x² + 1
1
2
x² + 1
y = (x²-4)³(2x² + 5) ³.
. (See](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46219ade-f670-4bb9-9a69-967c727b5c4e%2Fb2ee0c8f-6b61-42d5-bb31-8c1892200955%2Fzyi79e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:EXERCISES 3.1
Differentiate the functions in Exercises 1-28.
1. y= (x+1)(x3 +5x+2) 2. y = (-x³ +
3. y = (2x4x + 1)(-x³ + 1) 4. y = (x² + x + 1)³(x - 1)4
5. y = x(x² + 1)4
6. y=x√x
7. y = (x²+3)(x²-3) 10
8. y=[(-2x³ + x)(6x -
9. y= (5x+1)(x2 − 1) +
10. y = x²(3x4 + 12x - 1)²
x-1
11. y=
x+1
13. y =
15. y=
17. y =
19. y =
22. y=
23. y=
x² - 1
x² +1
x+3
(2x + 1)²
25. y =
1
TT
+
2
x² + 1
y=(x+11)'
x²
(x² + 1)²
21. y = [(3x² + 2x + 2)(x-2)]²
1
√x-2
1
Vx+1
2x + 1
3
27. y = √x + 2(2x + 1)²
12. y =
14. y =
X
x +
16. y=x² + 4x
18. y=
20. y =
24. y =
26. y =
+ 2)( ½ − 1)
28. y=
1
x²+x+7
ax + b
cx + d
(x + 1)³
(x - 5)²
3
√√x+1
x+3
x² + 1
√3x - 1
x
-3)]4
29. Find the equation of the tangent line to the curve
y = (x-2)(x + 1)² at the point (3, 16).
30. Find the equation of the tangent line to the curve
y = (x + 1)/(x - 1) at the point (2, 3).
31. Find all x-coordinates of points (x, y) on the curve
y = (x-2)/(x-4)³ where the tangent line is horizontal.
32. Find the inflection points on the graph of y=-
Fig. 2.)
Figure 2
33. Find all x such that
dy
dx
1
Y
y =
= 0, where
1
x² + 1
1
2
x² + 1
y = (x²-4)³(2x² + 5) ³.
. (See
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