College Algebra 7th Edition
ISBN: 9781305115545
Author: James Stewart, Lothar Redlin, Saleem Watson
Publisher: James Stewart, Lothar Redlin, Saleem Watson
P Prerequisites 1 Equations And Graphs 2 Functions 3 Polynomial And Rational Functions 4 Exponential And Logarithmic Functions 5 Systems Of Equations And Inequalities 6 Matrices And Determinants 7 Conic Sections 8 Sequences And Series 9 Counting And Probability A Calculations And Significant Figures B Graphing With A Graphing Calculator Chapter4: Exponential And Logarithmic Functions
4.1 Exponential Functions 4.2 The Natural Exponential Function 4.3 Logarithmic Functions 4.4 Laws Of Logarithms 4.5 Exponential And Logarithmic Equations 4.6 Modeling With Exponential Functions 4.7 Logarithmic Scales Chapter Questions Section: Chapter Questions
Problem 1CC Problem 2CC: Let f be The exponential function f(x)=ax , where a0 . (a) What is the function of f? (b) What is... Problem 3CC: If xis large, which function grows faster, f(x)=2x or g(x)=x2? Problem 4CC: (a) How is the number e defined? (b) Given an approximate value of e, rounded to five decimal... Problem 5CC Problem 6CC Problem 7CC Problem 8CC Problem 9CC Problem 10CC Problem 11CC Problem 12CC: Suppose that the initial size of a population is n0 and the population grows exponentially. Let n(t)... Problem 13CC Problem 14CC Problem 15CC: What is the logarithmic scale? If we use a logarithmic scale with base 10 what do the following... Problem 16CC Problem 17CC Problem 18CC Problem 1E Problem 2E Problem 3E Problem 4E Problem 5E Problem 6E Problem 7E Problem 8E Problem 9E Problem 10E Problem 11E Problem 12E Problem 13E Problem 14E Problem 15E Problem 16E: Graphing Exponential and Logarithmic functions Sketch the graph of the function. State the domain,... Problem 17E Problem 18E Problem 19E: Domain Find the domain of the function. h(x)=In(x24) Problem 20E Problem 21E: Exponential Form Write the equation in exponential form. log21024=10 Problem 22E Problem 23E Problem 24E Problem 25E: Logarithmic Form Write the equation in logarithmic form. 26=64 Problem 26E Problem 27E Problem 28E Problem 29E Problem 30E Problem 31E Problem 32E Problem 33E Problem 34E Problem 35E Problem 36E Problem 37E Problem 38E: Evaluating Logarithmic Expressions Evaluate the expression without using a calculate. e2In7 Problem 39E Problem 40E: Evaluating Logarithmic Expressions Evaluate the expression without using a calculate. log3243 Problem 41E Problem 42E Problem 43E Problem 44E Problem 45E Problem 46E Problem 47E Problem 48E Problem 49E Problem 50E Problem 51E Problem 52E Problem 53E Problem 54E Problem 55E Problem 56E Problem 57E Problem 58E Problem 59E Problem 60E Problem 61E Problem 62E Problem 63E Problem 64E Problem 65E Problem 66E Problem 67E Problem 68E Problem 69E Problem 70E Problem 71E Problem 72E Problem 73E Problem 74E Problem 75E Problem 76E: Local Extrema and Asymptotes Draw a graph of the function and use it to determine the asymptotes and... Problem 77E Problem 78E Problem 79E Problem 80E Problem 81E Problem 82E Problem 83E Problem 84E Problem 85E Problem 86E Problem 87E Problem 88E Problem 89E Problem 90E Problem 91E: Compound Interest If $12,000 is invested at an interest rate of 10% per year, find the amount of the... Problem 92E Problem 93E Problem 94E Problem 95E Problem 96E Problem 97E: Cat Population The stray-cat population in a small towngrows exponentially. In 1999 the town had 30... Problem 98E Problem 99E: Radioactive decay Uranium-234 has a half-life of 2.7x105 Years. (a)Find the amount remaining from a... Problem 100E Problem 101E: Radioactive Decay The half-life of radium-226 is 1590 years. (a)If a sample has a mass of 150 mg,... Problem 102E Problem 103E Problem 104E Problem 105E: pH The hydrogen ion concentration of fresh egg whites was measured as [H+]=1.3x108M Find the pH, and... Problem 106E Problem 107E Problem 108E Problem 1T Problem 2T Problem 3T Problem 4T Problem 5T Problem 6T Problem 7T Problem 8T Problem 9T Problem 10T: The initialsize of a culture of bacteria is 1000. After 1 hour the bacteria count is 8000. (a) Find... Problem 11T: Suppose that $12,000 is invested in a saving account paying 5.6% interest per year. (a)Write the... Problem 12T Problem 13T Problem 1P Problem 2P Problem 3P Problem 4P: The Beer-Lambert Law As sunlight passes through the waters of lakes and oceans, thelight isabsorbed,... Problem 5P Problem 6P: Modelling the species area relationship that table gives the area of several caves in Central Mexico... Problem 7P Problem 8P Problem 9P Problem 10P: Logistic Population growth the table and scatter plot give the population of black flies in a closed... Problem 3CC: If xis large, which function grows faster, f(x)=2x or g(x)=x2?
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Find the critical values of f then use the second derivative to determine if f has a relative maximum or relative minimum at each critical value.
Transcribed Image Text: In this probem you will apply the second derivative test to test the function f(x):
20
5x +
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
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