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...
Related questions
Question
23 and 31
![571
Section 127 Higher-Order Dervatives
%3D
Since y= e+y(the original equation).
tain
%3D
%3D
xp
2.
xp
)-
(2- y)
(器)
dx2
(2 y)
()
Now we express our answer without dy/dx. Since
2.
2 y
dx2
(2 – y)?
(2 – y)3
Now Work Problem 31 4
PROBLEMS 12.7
27. a x+b Jy=c
29. xy + y – x = 4
28. y- 6xy = 4
30. x² + 2xy + y² = 1
32. e + e = x² + y²
(2)
-
the derivative
at is, in terms
31. y = er+y
33. If x + 3x + y² = 4y, find d²y/dx² when x = 0 and y = 0.
34. Show that the equation
d²y
3. y = 8 – x,
dx?
4. y = -x – xr²,
dx?
substituting
d'F
6. F(q) = In (q + 1),
f"(x) + 4f'(x) + 4f(x) = 0
7. f(x) = x² In x, f"(x)
8. y =
is satisfied if f (x) = (3x – 5)e-2.
35. Find the rate of change of f'(x) if f(x) = (5x – 3)*.
%3D
36. Find the rate of change of f"(x) if
(b)„f• (b)f 6
(x),f'X^ = (x)f '0I
n),
1.
+ x^9 = (x)f
(4) „f 'd – 6^ = (4)f 'II
12. y = ear, y"
14. y = (3x +7)', y"
37. Marginal Cost If c = 0.2q? + 2q + 500 is a cost function,
how fast is marginal cost changing when q = 97.357?
13. y =
2r + 3' dx?
I + x
15. y =-1'
38. Marginal Revenue If p= 400 – 40g – q² is a demand
equation, how fast is marginal revenue changing when q = 4?
16. y = 2r/2 + (2x)/2, y"
x –
(2x + 5)(5x - 2)
39. If f(x) = x - 6x2 + 5x – 6, determine the values of x for
which f"(x) = 0.
18. y= In
17. y = In [x(x +a)], y"
%3D
x d'y
40. Suppose that e = y e*. (a) Determine dy/dx, and express
your answer in terms of y only. (b) Determine d²y/dx², and
express your answer in terms of y only.
20. y =
%3D
er' dx²
%3D
In Problems 41 and 42, determine f"(x). Then use your graphing
calculator to find all real roots of f"(x) = 0. Round your answers
to two decimal places.
21. If y = e2r + er, find
%3D
22. If y = e2In (x*+), find y" when x = 1.
%3D
In Problems 23–32, find y".
41. f(x) = 6e* – x³ – 15x²
23. x² + 4y² – 16 = 0
24. x2 - y? = 16
%3D
42. f(x) =
12
25. y² = 4x
26. 9x² + 16y² = 25
2.
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e2d6f28-e3d7-414c-b1d4-a752131175c2%2F4b865af5-625b-4fde-8424-6e1abc73f597%2F85ihsla.jpeg&w=3840&q=75)
Transcribed Image Text:571
Section 127 Higher-Order Dervatives
%3D
Since y= e+y(the original equation).
tain
%3D
%3D
xp
2.
xp
)-
(2- y)
(器)
dx2
(2 y)
()
Now we express our answer without dy/dx. Since
2.
2 y
dx2
(2 – y)?
(2 – y)3
Now Work Problem 31 4
PROBLEMS 12.7
27. a x+b Jy=c
29. xy + y – x = 4
28. y- 6xy = 4
30. x² + 2xy + y² = 1
32. e + e = x² + y²
(2)
-
the derivative
at is, in terms
31. y = er+y
33. If x + 3x + y² = 4y, find d²y/dx² when x = 0 and y = 0.
34. Show that the equation
d²y
3. y = 8 – x,
dx?
4. y = -x – xr²,
dx?
substituting
d'F
6. F(q) = In (q + 1),
f"(x) + 4f'(x) + 4f(x) = 0
7. f(x) = x² In x, f"(x)
8. y =
is satisfied if f (x) = (3x – 5)e-2.
35. Find the rate of change of f'(x) if f(x) = (5x – 3)*.
%3D
36. Find the rate of change of f"(x) if
(b)„f• (b)f 6
(x),f'X^ = (x)f '0I
n),
1.
+ x^9 = (x)f
(4) „f 'd – 6^ = (4)f 'II
12. y = ear, y"
14. y = (3x +7)', y"
37. Marginal Cost If c = 0.2q? + 2q + 500 is a cost function,
how fast is marginal cost changing when q = 97.357?
13. y =
2r + 3' dx?
I + x
15. y =-1'
38. Marginal Revenue If p= 400 – 40g – q² is a demand
equation, how fast is marginal revenue changing when q = 4?
16. y = 2r/2 + (2x)/2, y"
x –
(2x + 5)(5x - 2)
39. If f(x) = x - 6x2 + 5x – 6, determine the values of x for
which f"(x) = 0.
18. y= In
17. y = In [x(x +a)], y"
%3D
x d'y
40. Suppose that e = y e*. (a) Determine dy/dx, and express
your answer in terms of y only. (b) Determine d²y/dx², and
express your answer in terms of y only.
20. y =
%3D
er' dx²
%3D
In Problems 41 and 42, determine f"(x). Then use your graphing
calculator to find all real roots of f"(x) = 0. Round your answers
to two decimal places.
21. If y = e2r + er, find
%3D
22. If y = e2In (x*+), find y" when x = 1.
%3D
In Problems 23–32, find y".
41. f(x) = 6e* – x³ – 15x²
23. x² + 4y² – 16 = 0
24. x2 - y? = 16
%3D
42. f(x) =
12
25. y² = 4x
26. 9x² + 16y² = 25
2.
%3D
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