18. Test for concavity 19. Second derivative test 20. Inflection points 21. Inflection point test CHAPTER 4 MISCELLANEOUS PROBLEMS 2 x³y² = x+y 4 r² + y² = xy 6. √xy=√x+y Find dy/dx in Problems 1 through 6 1. = sin² y 3 +7=4 5-²+²-³-4 In Problems 2 through 10, write an equation of the line tangent to the given curve at the indicated point 7. xy-x-y=1; (0,-1) &x=sin 2y: (1.x/4) 9. ²-3xy+2y² = 0; (2,1) 10, y¹=¹+; (0,0) In Problems 11 through 16, write dy in terms of x and dx. 11. y= (4x-²)/2 12. y = 8√√² +9 13. y = x=1 14. y = sin x² 15. y = x² cos √ 16. y = sin 2x In Problems 17 through 26, estimate the indicated number by linear approximation. 27. If the mean value theorem applies to the function on the val (a, b), it ensures the existence of a solution c in the (a, b) of the equation f'(c) = b-a 33. f(x)=x-[1.3] 34. f(x)=x²+x-4; [-2,3] 35. f(x)=x²; [-1.2] 37. f(x)=x: [-1,2] 65f0 67. f(x)=x In Problems 33 through 38, a function f and an interva are given. Verify that the hypotheses of the mean val are satisfied for fon (a, b). Then use the given equation the value of the number c. 69. f(x) 71. f(x)= 73. f(x) 3 75. f(x) 77. f(x)= 78. f(x) = 36. f(x)=x²¹: 1-2 38. f(x)=√x: (84 24 2 Sketch the graphs of the functions in Problems 39 throug Indicate the local maxima and minima of each functio the intervals on which the function is increasing or decr Show the concave structure of the graph and identity d tion points. ₂ 40 fix-20 11 14 and 79. fl 80. 81. f 82. 83.
18. Test for concavity 19. Second derivative test 20. Inflection points 21. Inflection point test CHAPTER 4 MISCELLANEOUS PROBLEMS 2 x³y² = x+y 4 r² + y² = xy 6. √xy=√x+y Find dy/dx in Problems 1 through 6 1. = sin² y 3 +7=4 5-²+²-³-4 In Problems 2 through 10, write an equation of the line tangent to the given curve at the indicated point 7. xy-x-y=1; (0,-1) &x=sin 2y: (1.x/4) 9. ²-3xy+2y² = 0; (2,1) 10, y¹=¹+; (0,0) In Problems 11 through 16, write dy in terms of x and dx. 11. y= (4x-²)/2 12. y = 8√√² +9 13. y = x=1 14. y = sin x² 15. y = x² cos √ 16. y = sin 2x In Problems 17 through 26, estimate the indicated number by linear approximation. 27. If the mean value theorem applies to the function on the val (a, b), it ensures the existence of a solution c in the (a, b) of the equation f'(c) = b-a 33. f(x)=x-[1.3] 34. f(x)=x²+x-4; [-2,3] 35. f(x)=x²; [-1.2] 37. f(x)=x: [-1,2] 65f0 67. f(x)=x In Problems 33 through 38, a function f and an interva are given. Verify that the hypotheses of the mean val are satisfied for fon (a, b). Then use the given equation the value of the number c. 69. f(x) 71. f(x)= 73. f(x) 3 75. f(x) 77. f(x)= 78. f(x) = 36. f(x)=x²¹: 1-2 38. f(x)=√x: (84 24 2 Sketch the graphs of the functions in Problems 39 throug Indicate the local maxima and minima of each functio the intervals on which the function is increasing or decr Show the concave structure of the graph and identity d tion points. ₂ 40 fix-20 11 14 and 79. fl 80. 81. f 82. 83.
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![18. Test for concavity
19, Second derivative test
20. Inflection points
21. Inflection point test
CHAPTER 4 MISCELLANEOUS PROBLEMS
Find dy/dx in Problems 1 through 6
1. = sin² y
3
+7=4
5-²+²-³-4
2 x³y² = x+y
4 r²+y=xy
6 √xy=√x+y
In Problems 2 through 10, write an equation of the line tangent
to the given curve at the indicated point.
7. xy-x-y=1; (0,-1)
&x=sin 2y: (1.x/4)
9.x²-3xy+2y² = 0; (2,1)
10. y'=+; (0,0)
In Problems 11 through 16, write dy in terms of x and dx.
11. y= (4x-²)/2
12. y = 8x³√²+9
14. y = sin x²
x+1
13 y=+=
15. y = x² cos √x
16. y=
sin 2x
In Problems 17 through 26, estimate the indicated number by
linear approximation.
27.
If the mean value theorem applies to the function on the
val (a, b), it ensures the existence of a solution c in the
(a, b) of the equation
f'(c) =
b-a
33. f(x)=x-
34. f(x)=x²+x-4; [-2,3]
35. f(x)=x²; [-1.2]
37. f(x)=x: [-1,2]
65 10
67. f(x)=x
In Problems 33 through 38, a function f and an interva
are given. Verify that the hypotheses of the mean val
are satisfied for fon (a, b). Then use the given equation
the value of the number c.
[1.3]
69. f(x)
71. f(x)=
73. f(x)=3
36. f(x)=x²¹: 1-2
38. f(x)=√x: (84
4
75. f(x)
77. f(x)=
78. f(x) =
Sketch the graphs of the functions in Problems 39 throu
Indicate the local maxima and minima of each function
the intervals on which the function is increasing or decr
Show the concave structure of the graph and identity d
tion points.
40 fix-20 21
14
and
79. fl
80.
81. f
82.
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Transcribed Image Text:18. Test for concavity
19, Second derivative test
20. Inflection points
21. Inflection point test
CHAPTER 4 MISCELLANEOUS PROBLEMS
Find dy/dx in Problems 1 through 6
1. = sin² y
3
+7=4
5-²+²-³-4
2 x³y² = x+y
4 r²+y=xy
6 √xy=√x+y
In Problems 2 through 10, write an equation of the line tangent
to the given curve at the indicated point.
7. xy-x-y=1; (0,-1)
&x=sin 2y: (1.x/4)
9.x²-3xy+2y² = 0; (2,1)
10. y'=+; (0,0)
In Problems 11 through 16, write dy in terms of x and dx.
11. y= (4x-²)/2
12. y = 8x³√²+9
14. y = sin x²
x+1
13 y=+=
15. y = x² cos √x
16. y=
sin 2x
In Problems 17 through 26, estimate the indicated number by
linear approximation.
27.
If the mean value theorem applies to the function on the
val (a, b), it ensures the existence of a solution c in the
(a, b) of the equation
f'(c) =
b-a
33. f(x)=x-
34. f(x)=x²+x-4; [-2,3]
35. f(x)=x²; [-1.2]
37. f(x)=x: [-1,2]
65 10
67. f(x)=x
In Problems 33 through 38, a function f and an interva
are given. Verify that the hypotheses of the mean val
are satisfied for fon (a, b). Then use the given equation
the value of the number c.
[1.3]
69. f(x)
71. f(x)=
73. f(x)=3
36. f(x)=x²¹: 1-2
38. f(x)=√x: (84
4
75. f(x)
77. f(x)=
78. f(x) =
Sketch the graphs of the functions in Problems 39 throu
Indicate the local maxima and minima of each function
the intervals on which the function is increasing or decr
Show the concave structure of the graph and identity d
tion points.
40 fix-20 21
14
and
79. fl
80.
81. f
82.
83.
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