Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)
11th Edition
ISBN: 9780133886832
Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey
Publisher: PEARSON
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Chapter 4, Problem 13RE
To determine
To find: The derivative of the given function using rules for derivative.
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Exercise 11.3 A slope field is given for the equation y' = 4y+4.
(a) Sketch the particular solution that corresponds to y(0) = −2
(b) Find the constant solution
(c) For what initial conditions y(0) is the solution increasing?
(d) For what initial conditions y(0) is the solution decreasing?
(e) Verify these results using only the differential equation y' = 4y+4.
Chapter 4 Solutions
Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)
Ch. 4.1 - YOUR TURN 1 find f′(t).
Ch. 4.1 - YOUR TURN 2 find dy/dx.
Ch. 4.1 - Prob. 3YTCh. 4.1 - Prob. 4YTCh. 4.1 - Prob. 5YTCh. 4.1 - Prob. 1WECh. 4.1 - Prob. 2WECh. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...
Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Prob. 21ECh. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - 23. Which of the following describes the...Ch. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - Find each derivative.
27.
Ch. 4.1 - Find each derivative.
28.
Ch. 4.1 - Prob. 29ECh. 4.1 - Find each derivative.
30.f′(3) if
Ch. 4.1 - In Exercises 31-34, find the slope of the tangent...Ch. 4.1 - In Exercises 31-34, find the slope of the tangent...Ch. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - In Exercises 37-40, for each function find all...Ch. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - In Exercises 37-40, for each function find all...Ch. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - 44. If g′(5) = 12 and h′ (5) = −3, find f′ (5) for...Ch. 4.1 - Prob. 45ECh. 4.1 - 46. Use the information given in the figure to...Ch. 4.1 - Prob. 47ECh. 4.1 - Prob. 48ECh. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Prob. 53ECh. 4.1 - Prob. 54ECh. 4.1 - Prob. 55ECh. 4.1 - Prob. 56ECh. 4.1 - Prob. 57ECh. 4.1 - Prob. 58ECh. 4.1 - Prob. 59ECh. 4.1 - Prob. 60ECh. 4.1 - Prob. 61ECh. 4.1 - Prob. 62ECh. 4.1 - Prob. 63ECh. 4.1 - Prob. 64ECh. 4.1 - 65. Track and Field In 1906 Kennelly developed a...Ch. 4.1 - Prob. 66ECh. 4.1 - Prob. 67ECh. 4.1 - Prob. 68ECh. 4.1 - Prob. 69ECh. 4.1 - Velocity We saw in the previous chapter that if a...Ch. 4.1 - Prob. 71ECh. 4.1 - Prob. 72ECh. 4.1 - 73. Velocity A ball is thrown vertically upward...Ch. 4.1 - 74. Dead Sea Researchers who have been studying...Ch. 4.1 - Prob. 75ECh. 4.1 - 76. AP Examination The probability (as a percent)...Ch. 4.1 - 77. Dog’s Human Age From the data printed in the...Ch. 4.2 - YOUR TURN 1 Find the derivative of y = (x3 + 7)(4...Ch. 4.2 - YOUR TURN 2 Find f′(x) if
Ch. 4.2 - Prob. 3YTCh. 4.2 - Prob. 4YTCh. 4.2 - Prob. 1WECh. 4.2 - Prob. 2WECh. 4.2 - Prob. 3WECh. 4.2 - Prob. 1ECh. 4.2 - Use the product rule to find the derivative of the...Ch. 4.2 - Use the product rule to find the derivative of the...Ch. 4.2 - Use the product rule to find the derivative of the...Ch. 4.2 - Use the product rule to find the derivative of the...Ch. 4.2 - Use the product rule to find the derivative of the...Ch. 4.2 - Use the product rule to find the derivative of the...Ch. 4.2 - Use the product rule to find the derivative of the...Ch. 4.2 - Use the product rule to find the derivative of the...Ch. 4.2 - Use the product rule to find the derivative of the...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Prob. 25ECh. 4.2 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Prob. 29ECh. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - 34. Find an equation of the line tangent to the...Ch. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Prob. 37ECh. 4.2 - 38. Use the fact that f(x) = u(x)/v(x) can be...Ch. 4.2 - Prob. 39ECh. 4.2 - Prob. 40ECh. 4.2 - Prob. 41ECh. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Prob. 44ECh. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.2 - Prob. 47ECh. 4.2 - 48. Revenue Suppose that at the beginning of the...Ch. 4.2 - Prob. 49ECh. 4.2 - 50. Muscle Reaction When a certain drug is...Ch. 4.2 - Prob. 51ECh. 4.2 - Prob. 52ECh. 4.2 - Prob. 53ECh. 4.2 - 54. Memory Retention Some psychologists contend...Ch. 4.2 - Prob. 55ECh. 4.2 - Prob. 56ECh. 4.3 - YOUR TURN 1 For the functionsin Example 1, find...Ch. 4.3 - Prob. 2YTCh. 4.3 - Prob. 3YTCh. 4.3 - Prob. 4YTCh. 4.3 - Prob. 5YTCh. 4.3 - Prob. 6YTCh. 4.3 - Prob. 7YTCh. 4.3 - Prob. 1WECh. 4.3 - Prob. 2WECh. 4.3 - Prob. 3WECh. 4.3 - Prob. 1ECh. 4.3 - Let f(x) = 5x2 − 2x and g(x) = 8x + 3.
2....Ch. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Find f[g(x)] and g[f(x)].
8. f(x) = −8x + 9;
Ch. 4.3 - Prob. 9ECh. 4.3 - Prob. 10ECh. 4.3 - Prob. 11ECh. 4.3 - Find f[g(x)] and g[f(x)].
12. f(x) = 8x2 − 11x;
Ch. 4.3 - Find f[g(x)] and g[f(x)].
13. ;
Ch. 4.3 - Find f[g(x)] and g[f(x)].
14. ;
Ch. 4.3 - Prob. 15ECh. 4.3 - Write each function as the composition of two...Ch. 4.3 - Prob. 17ECh. 4.3 - Write each function as the composition of two...Ch. 4.3 - Prob. 19ECh. 4.3 - Write each function as the composition of two...Ch. 4.3 - Prob. 21ECh. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - Prob. 44ECh. 4.3 - Prob. 45ECh. 4.3 - In Exercises 45-48, find the equation of the...Ch. 4.3 - Prob. 47ECh. 4.3 - Prob. 48ECh. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - 52. Mrugy and Nate are working on taking the...Ch. 4.3 - Prob. 53ECh. 4.3 - Prob. 54ECh. 4.3 - Prob. 55ECh. 4.3 - 56. Demand Suppose a demand function is given...Ch. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - Prob. 59ECh. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - 63. To test an individual’s use of calcium, a...Ch. 4.3 - Prob. 64ECh. 4.4 - YOUR TURN 1 Find dy/dx for
y = 43x,
y = e3x+5.
Ch. 4.4 - Prob. 2YTCh. 4.4 - Prob. 3YTCh. 4.4 - Prob. 4YTCh. 4.4 - Prob. 1WECh. 4.4 - Prob. 2WECh. 4.4 - Prob. 3WECh. 4.4 - Prob. 1ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Prob. 7ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - Prob. 12ECh. 4.4 - Prob. 13ECh. 4.4 - Prob. 14ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 21ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 24ECh. 4.4 - Prob. 25ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 32ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 35ECh. 4.4 - Prob. 36ECh. 4.4 - Prob. 37ECh. 4.4 - Prob. 38ECh. 4.4 - Prob. 39ECh. 4.4 - 40. Sales The sales of a new personal computer (in...Ch. 4.4 - Prob. 41ECh. 4.4 - Prob. 42ECh. 4.4 - Prob. 43ECh. 4.4 - 44. Investment The value of a particular...Ch. 4.4 - Prob. 45ECh. 4.4 - 46. Population Growth In Section 10.4, Exercise...Ch. 4.4 - Prob. 47ECh. 4.4 - Prob. 48ECh. 4.4 - Prob. 49ECh. 4.4 - Prob. 50ECh. 4.4 - Prob. 52ECh. 4.4 - Prob. 53ECh. 4.4 - Prob. 54ECh. 4.4 - Prob. 55ECh. 4.4 - Prob. 56ECh. 4.4 - Prob. 57ECh. 4.4 - Prob. 58ECh. 4.4 - Prob. 59ECh. 4.4 - Prob. 60ECh. 4.4 - Prob. 61ECh. 4.4 - Prob. 62ECh. 4.4 - 63. The Gateway Arch The Gateway Arch in St....Ch. 4.4 - Prob. 64ECh. 4.4 - Prob. 65ECh. 4.5 - YOUR TURN 1 Find the derivative of f(x) = log3x.
Ch. 4.5 - Prob. 2YTCh. 4.5 - Prob. 3YTCh. 4.5 - Prob. 1WECh. 4.5 - Prob. 2WECh. 4.5 - Prob. 3WECh. 4.5 - Prob. 1ECh. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - Find the derivative of each function.
4. y = ln(1...Ch. 4.5 - Prob. 5ECh. 4.5 - Find the derivative of each function.
6. y =...Ch. 4.5 - Prob. 7ECh. 4.5 - Prob. 8ECh. 4.5 - Find the derivative of each function.
9.
Ch. 4.5 - Prob. 10ECh. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Prob. 13ECh. 4.5 - Prob. 14ECh. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Prob. 19ECh. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Prob. 24ECh. 4.5 - Prob. 25ECh. 4.5 - Prob. 26ECh. 4.5 - Prob. 27ECh. 4.5 - Prob. 28ECh. 4.5 - Prob. 29ECh. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Prob. 32ECh. 4.5 - Prob. 33ECh. 4.5 - Prob. 34ECh. 4.5 - Prob. 35ECh. 4.5 - Prob. 36ECh. 4.5 - Prob. 37ECh. 4.5 - Prob. 38ECh. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Prob. 40ECh. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Find the derivative of each of the following...Ch. 4.5 - Prob. 45ECh. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Prob. 48ECh. 4.5 - Prob. 49ECh. 4.5 - Prob. 50ECh. 4.5 - Prob. 51ECh. 4.5 - Prob. 52ECh. 4.5 - Prob. 53ECh. 4.5 - Use the ideas from Exercise 53 to find the...Ch. 4.5 - Prob. 55ECh. 4.5 - Prob. 56ECh. 4.5 - 57. Revenue Suppose the demand function for q...Ch. 4.5 - 58. Profit If the cost function in dollars for q...Ch. 4.5 - Prob. 59ECh. 4.5 - Prob. 60ECh. 4.5 - Prob. 61ECh. 4.5 - Prob. 62ECh. 4.5 - Prob. 63ECh. 4.5 - Prob. 64ECh. 4.5 - Prob. 65ECh. 4.5 - Prob. 66ECh. 4.5 - 67. Richter Scale Richter Scale The Richter scale...Ch. 4.5 - Prob. 68ECh. 4 - Prob. 1RECh. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Use the rules for derivatives to find the...Ch. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Use the rules for derivatives to find the...Ch. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - Use the rules for derivatives to find the...Ch. 4 - Prob. 45RECh. 4 - Prob. 46RECh. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - Prob. 49RECh. 4 - Prob. 50RECh. 4 - Prob. 51RECh. 4 - Prob. 52RECh. 4 - Prob. 53RECh. 4 - Prob. 54RECh. 4 - Prob. 55RECh. 4 - Prob. 56RECh. 4 - Prob. 57RECh. 4 - Prob. 58RECh. 4 - Prob. 59RECh. 4 - Prob. 60RECh. 4 - Find the slope of the tangent line to the given...Ch. 4 - Prob. 62RECh. 4 - Prob. 63RECh. 4 - Prob. 64RECh. 4 - Prob. 65RECh. 4 - Prob. 66RECh. 4 - Prob. 67RECh. 4 - Prob. 68RECh. 4 - Prob. 69RECh. 4 - Prob. 70RECh. 4 - Prob. 71RECh. 4 - Prob. 72RECh. 4 - Prob. 73RECh. 4 - Prob. 74RECh. 4 - Prob. 75RECh. 4 - Prob. 76RECh. 4 - Prob. 77RECh. 4 - Prob. 78RECh. 4 - Prob. 79RECh. 4 - Prob. 80RECh. 4 - Prob. 81RECh. 4 - Prob. 83RECh. 4 - Prob. 84RECh. 4 - Prob. 85RECh. 4 - Prob. 86RECh. 4 - Prob. 87RECh. 4 - Prob. 88RECh. 4 - Prob. 89RECh. 4 - Prob. 90RECh. 4 - Prob. 91RECh. 4 - Prob. 92RECh. 4 - Prob. 93RE
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