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Math Calculus Calculus For The Life Sciences

Using the definition of the derivative, find f ' ( x ) . Then find f ' ( − 2 ) , f ' ( 0 ) , and f ' ( 3 ) when the derivative exists. ( Hint for Exercises 17 and 18 : In step 3, multiply numerator and denominator by x + h + x .) f ( x ) = − 3 x .

Using the definition of the derivative, find f ' ( x ) . Then find f ' ( − 2 ) , f ' ( 0 ) , and f ' ( 3 ) when the derivative exists. ( Hint for Exercises 17 and 18 : In step 3, multiply numerator and denominator by x + h + x .) f ( x ) = − 3 x .

Solution Summary: The author explains that the function f(x)=-3sqrtx is not defined.

Calculus For The Life Sciences

Calculus For The Life Sciences

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Concept explainers

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Textbook Question

Chapter 3.4, Problem 18E

Using the definition of the derivative, find f ' ( x ) . Then find f ' ( − 2 ) , f ' ( 0 ) , and f ' ( 3 ) when the derivative exists. (Hint for Exercises 17 and 18: In step 3, multiply numerator and denominator by x + h + x .)

f ( x ) = − 3 x .

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Chapter 3.4, Problem 17E

Chapter 3.4, Problem 19E

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Chapter 3 Solutions

Calculus For The Life Sciences

Ch. 3.1 - Find limx1(x2+2).Ch. 3.1 - Find limx2x24x2.Ch. 3.1 - Find limx3f(x) if f(x)={2x1ifx31ifx=3.Ch. 3.1 - Prob. 4YT Ch. 3.1 - Prob. 5YT Ch. 3.1 - Prob. 6YT Ch. 3.1 - Prob. 7YT Ch. 3.1 - Prob. 8YT Ch. 3.1 - In Excercises 1-4, choose the best answer for each...Ch. 3.1 - Prob. 2E

Ch. 3.1 - In Excercises 1-4, choose the best answer for each...Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Decide whether each limit exists. If a limit...Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - In Exercise 9 and 10, use the graph to find i...Ch. 3.1 - Decide whether each limit exists. If a limit...Ch. 3.1 - Decide whether each limit exists. If a limit...Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Complete the tables and use the results to find...Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Let limx4f(x)=9and limx4g(x)=27. Use the limit...Ch. 3.1 - Let limx4f(x)=9and limx4g(x)=27. Use the limit...Ch. 3.1 - Prob. 26E Ch. 3.1 - Let limx4f(x)=9and limx4g(x)=27. Use the limit...Ch. 3.1 - Let limx4f(x)=9and limx4g(x)=27. Use the limit...Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 49E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 51E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 53E Ch. 3.1 - Use the properties of limits to help decide...Ch. 3.1 - Prob. 55E Ch. 3.1 - Prob. 56E Ch. 3.1 - Prob. 57E Ch. 3.1 - Prob. 58E Ch. 3.1 - Prob. 59E Ch. 3.1 - Prob. 60E Ch. 3.1 - Prob. 61E Ch. 3.1 - Prob. 62E Ch. 3.1 - Prob. 63E Ch. 3.1 - Prob. 64E Ch. 3.1 - Prob. 65E Ch. 3.1 - Prob. 66E Ch. 3.1 - Prob. 67E Ch. 3.1 - Let G(x)=6(x4)2. a. Find limx4G(x). b. Find the...Ch. 3.1 - Prob. 69E Ch. 3.1 - Prob. 70E Ch. 3.1 - Prob. 71E Ch. 3.1 - Use a graphing calculator to answer the following...Ch. 3.1 - Prob. 73E Ch. 3.1 - Prob. 74E Ch. 3.1 - Explain in your own words why the rules for limits...Ch. 3.1 - Prob. 76E Ch. 3.1 - Prob. 77E Ch. 3.1 - Prob. 78E Ch. 3.1 - Prob. 79E Ch. 3.1 - Prob. 80E Ch. 3.1 - Prob. 81E Ch. 3.1 - Prob. 82E Ch. 3.1 - Prob. 83E Ch. 3.1 - Prob. 84E Ch. 3.1 - Prob. 85E Ch. 3.1 - Prob. 86E Ch. 3.1 - Prob. 87E Ch. 3.1 - Prob. 88E Ch. 3.1 - Prob. 89E Ch. 3.1 - Prob. 90E Ch. 3.1 - Prob. 91E Ch. 3.1 - Drug Concentration The Concentration of a drug in...Ch. 3.1 - Alligator Teeth Researchers have developed a...Ch. 3.1 - Prob. 94E Ch. 3.1 - 95. Cell Surface Receptors In an article on the...Ch. 3.1 - Nervous system In a model of the nervous system,...Ch. 3.1 - Prob. 97E Ch. 3.1 - Employee Productivity A company training program...Ch. 3.2 - Find all values of x where the function f(x)=5x+3...Ch. 3.2 - Prob. 2YT Ch. 3.2 - In Exercises 1-6, find all values x=a where the...Ch. 3.2 - In Exercises 1-6, find all values x=a where the...Ch. 3.2 - Prob. 3E Ch. 3.2 - In Exercises 1-6, find all values x=a where the...Ch. 3.2 - In Exercises 1-6, find all values x=a where the...Ch. 3.2 - Prob. 6E Ch. 3.2 - Prob. 7E Ch. 3.2 - Prob. 8E Ch. 3.2 - Prob. 9E Ch. 3.2 - Prob. 10E Ch. 3.2 - Prob. 11E Ch. 3.2 - Prob. 12E Ch. 3.2 - Prob. 13E Ch. 3.2 - Prob. 14E Ch. 3.2 - Prob. 15E Ch. 3.2 - Prob. 16E Ch. 3.2 - Find all values of x where the function is...Ch. 3.2 - Prob. 18E Ch. 3.2 - Prob. 19E Ch. 3.2 - Prob. 20E Ch. 3.2 - Prob. 21E Ch. 3.2 - In Exercises 21-26, a graph the given function, b...Ch. 3.2 - Prob. 23E Ch. 3.2 - In Exercises 21-26, a graph the given function, b...Ch. 3.2 - Prob. 25E Ch. 3.2 - Prob. 26E Ch. 3.2 - In Exercises 27-30, find the value of the constant...Ch. 3.2 - In Exercises 27-30, find the value of the constant...Ch. 3.2 - In Exercises 27-30, find the value of the constant...Ch. 3.2 - In Exercises 27-30, find the value of the constant...Ch. 3.2 - Prob. 31E Ch. 3.2 - Prob. 32E Ch. 3.2 - Prob. 33E Ch. 3.2 - Prob. 34E Ch. 3.2 - Prob. 35E Ch. 3.2 - Prob. 36E Ch. 3.2 - Prob. 37E Ch. 3.2 - Prob. 38E Ch. 3.2 - Prob. 39E Ch. 3.2 - Prob. 40E Ch. 3.2 - Poultry Farming Researchers at Iowa State...Ch. 3.2 - Prob. 42E Ch. 3.2 - Production The graph shows the profit from the...Ch. 3.2 - Cost Analysis The cost of ambulance transport...Ch. 3.2 - Prob. 45E Ch. 3.2 - Prob. 46E Ch. 3.3 - YOUR TURN Find the average rate of change in the...Ch. 3.3 - Prob. 2YT Ch. 3.3 - Prob. 3YT Ch. 3.3 - Prob. 4YT Ch. 3.3 - Prob. 1E Ch. 3.3 - Prob. 2E Ch. 3.3 - Prob. 3E Ch. 3.3 - Prob. 4E Ch. 3.3 - Find the average rate of change for each function...Ch. 3.3 - Find the average rate of change for each function...Ch. 3.3 - Find the average rate of change for each function...Ch. 3.3 - Prob. 8E Ch. 3.3 - Prob. 9E Ch. 3.3 - Prob. 10E Ch. 3.3 - Prob. 11E Ch. 3.3 - Prob. 12E Ch. 3.3 - Suppose the position function of an object moving...Ch. 3.3 - Suppose the position function of an object moving...Ch. 3.3 - Prob. 15E Ch. 3.3 - Prob. 16E Ch. 3.3 - Prob. 17E Ch. 3.3 - Prob. 18E Ch. 3.3 - Find the instantaneous rate of change for each...Ch. 3.3 - Find the instantaneous rate of change for each...Ch. 3.3 - Prob. 21E Ch. 3.3 - Prob. 22E Ch. 3.3 - Use the formula for instantaneous rate of change,...Ch. 3.3 - Use the formula for instantaneous rate of change,...Ch. 3.3 - Prob. 25E Ch. 3.3 - Prob. 26E Ch. 3.3 - Prob. 27E Ch. 3.3 - Use the formula for instantaneous rate of change,...Ch. 3.3 - Explain the difference between the average rate of...Ch. 3.3 - If the instantaneous rate of change of f(x) with...Ch. 3.3 - Flu Epidemic Epidemiologists in College Station,...Ch. 3.3 - Prob. 32E Ch. 3.3 - Bacterial Population The graph shows the...Ch. 3.3 - Thermic Effect of Food The metabolic rate of a...Ch. 3.3 - Molars The crown length as shown below of first...Ch. 3.3 - Mass of Bighorn Yearlings The body mass of...Ch. 3.3 - Minority Population The U.S. population is...Ch. 3.3 - Minority Population The U.S. Census population...Ch. 3.3 - Drug Use The chart on the next page shows how the...Ch. 3.3 - Prob. 40E Ch. 3.3 - Prob. 41E Ch. 3.3 - Immigration The following graph shows...Ch. 3.3 - Temperature The graph shows the temperature T in...Ch. 3.3 - Velocity A car is moving along a straight test...Ch. 3.3 - Prob. 45E Ch. 3.3 - Prob. 46E Ch. 3.3 - Prob. 47E Ch. 3.3 - Prob. 48E Ch. 3.4 - YOUR TURN For the graph of f(x)=x2x, a find the...Ch. 3.4 - Prob. 2YT Ch. 3.4 - Prob. 3YT Ch. 3.4 - Prob. 4YT Ch. 3.4 - YOUR TURN Let f(x)=2x. Find f(x).Ch. 3.4 - Prob. 6YT Ch. 3.4 - By considering, but not calculating, the slope of...Ch. 3.4 - Prob. 2E Ch. 3.4 - Prob. 3E Ch. 3.4 - Prob. 4E Ch. 3.4 - Prob. 5E Ch. 3.4 - Prob. 6E Ch. 3.4 - Estimate the slope of the tangent line to each...Ch. 3.4 - Estimate the slope of the tangent line to each...Ch. 3.4 - Estimate the slope of the tangent line to each...Ch. 3.4 - Estimate the slope of the tangent line to each...Ch. 3.4 - Prob. 11E Ch. 3.4 - Using the definition of the derivative, find f(x)....Ch. 3.4 - Using the definition of the derivative, find f(x)....Ch. 3.4 - Using the definition of the derivative, find f(x)....Ch. 3.4 - Using the definition of the derivative, find f(x)....Ch. 3.4 - Using the definition of the derivative, find f(x)....Ch. 3.4 - Using the definition of the derivative, find f(x)....Ch. 3.4 - Using the definition of the derivative, find f(x)....Ch. 3.4 - Prob. 19E Ch. 3.4 - Prob. 20E Ch. 3.4 - For each function, find a the equation of the...Ch. 3.4 - Prob. 22E Ch. 3.4 - For each function, find a the equation of the...Ch. 3.4 - Prob. 24E Ch. 3.4 - Prob. 25E Ch. 3.4 - Prob. 26E Ch. 3.4 - Prob. 27E Ch. 3.4 - Prob. 28E Ch. 3.4 - Prob. 29E Ch. 3.4 - Prob. 30E Ch. 3.4 - Prob. 31E Ch. 3.4 - Prob. 32E Ch. 3.4 - Prob. 33E Ch. 3.4 - Prob. 34E Ch. 3.4 - Prob. 35E Ch. 3.4 - Prob. 36E Ch. 3.4 - Prob. 37E Ch. 3.4 - Find the x- values where the following do not have...Ch. 3.4 - Prob. 39E Ch. 3.4 - Prob. 40E Ch. 3.4 - Prob. 41E Ch. 3.4 - Prob. 42E Ch. 3.4 - In Exercises 4245, find the derivative of the...Ch. 3.4 - Prob. 44E Ch. 3.4 - Prob. 45E Ch. 3.4 - Prob. 46E Ch. 3.4 - Prob. 47E Ch. 3.4 - Prob. 48E Ch. 3.4 - Prob. 49E Ch. 3.4 - Prob. 50E Ch. 3.4 - Prob. 51E Ch. 3.4 - Prob. 52E Ch. 3.4 - Prob. 53E Ch. 3.4 - Prob. 54E Ch. 3.4 - Temperature The graph shows the temperature in...Ch. 3.4 - Oven Temperature The graph shows the temperature...Ch. 3.4 - Prob. 57E Ch. 3.4 - Prob. 58E Ch. 3.4 - Social Security Assets The table gives actual and...Ch. 3.5 - Prob. 1YT Ch. 3.5 - Prob. 2YT Ch. 3.5 - Prob. 1E Ch. 3.5 - Prob. 2E Ch. 3.5 - Prob. 3E Ch. 3.5 - Prob. 4E Ch. 3.5 - Prob. 5E Ch. 3.5 - Each graphing calculator window shows the graph of...Ch. 3.5 - Sketch the graph of the derivative for each...Ch. 3.5 - Sketch the graph of the derivative for each...Ch. 3.5 - Sketch the graph of the derivative for each...Ch. 3.5 - Sketch the graph of the derivative for each...Ch. 3.5 - Sketch the graph of the derivative for each...Ch. 3.5 - Sketch the graph of the derivative for each...Ch. 3.5 - Prob. 13E Ch. 3.5 - Prob. 14E Ch. 3.5 - Prob. 15E Ch. 3.5 - Prob. 16E Ch. 3.5 - Prob. 17E Ch. 3.5 - 18. Flight Speed The graph shows the relationship...Ch. 3.5 - Human Growth The growth remaining in sitting...Ch. 3.5 - Prob. 20E Ch. 3.5 - Prob. 21E Ch. 3.5 - Body Mass Index The following graph shows how the...Ch. 3.5 - Prob. 23E Ch. 3.5 - Consumer Demand When the price of an essential...Ch. 3.5 - Prob. 25E Ch. 3.CR - Prob. 1CR Ch. 3.CR - Prob. 2CR Ch. 3.CR - Prob. 3CR Ch. 3.CR - Prob. 4CR Ch. 3.CR - Prob. 5CR Ch. 3.CR - Prob. 6CR Ch. 3.CR - Prob. 7CR Ch. 3.CR - Prob. 8CR Ch. 3.CR - Prob. 9CR Ch. 3.CR - Prob. 10CR Ch. 3.CR - Prob. 11CR Ch. 3.CR - Determine whether each of the following statements...Ch. 3.CR - Prob. 13CR Ch. 3.CR - Prob. 14CR Ch. 3.CR - Prob. 15CR Ch. 3.CR - Prob. 16CR Ch. 3.CR - Prob. 17CR Ch. 3.CR - Prob. 18CR Ch. 3.CR - Prob. 19CR Ch. 3.CR - Prob. 20CR Ch. 3.CR - Prob. 21CR Ch. 3.CR - Prob. 22CR Ch. 3.CR - Prob. 23CR Ch. 3.CR - Prob. 24CR Ch. 3.CR - Prob. 25CR Ch. 3.CR - Prob. 26CR Ch. 3.CR - Prob. 27CR Ch. 3.CR - Prob. 28CR Ch. 3.CR - Prob. 29CR Ch. 3.CR - Prob. 30CR Ch. 3.CR - Prob. 31CR Ch. 3.CR - Prob. 32CR Ch. 3.CR - Prob. 33CR Ch. 3.CR - Prob. 34CR Ch. 3.CR - Prob. 35CR Ch. 3.CR - Prob. 36CR Ch. 3.CR - Prob. 37CR Ch. 3.CR - Prob. 38CR Ch. 3.CR - Find all values x=a where the function is...Ch. 3.CR - Prob. 40CR Ch. 3.CR - Prob. 41CR Ch. 3.CR - Prob. 42CR Ch. 3.CR - Prob. 43CR Ch. 3.CR - Prob. 44CR Ch. 3.CR - Prob. 45CR Ch. 3.CR - Prob. 46CR Ch. 3.CR - Prob. 47CR Ch. 3.CR - Prob. 48CR Ch. 3.CR - Find each limit a by investigating values of the...Ch. 3.CR - Find each limit a by investigating values of the...Ch. 3.CR - Prob. 51CR Ch. 3.CR - Prob. 52CR Ch. 3.CR - Prob. 53CR Ch. 3.CR - Find the average rate of change for the following...Ch. 3.CR - Prob. 55CR Ch. 3.CR - Prob. 56CR Ch. 3.CR - Prob. 57CR Ch. 3.CR - Prob. 58CR Ch. 3.CR - Prob. 59CR Ch. 3.CR - Prob. 60CR Ch. 3.CR - Prob. 61CR Ch. 3.CR - Prob. 62CR Ch. 3.CR - Prob. 63CR Ch. 3.CR - Prob. 64CR Ch. 3.CR - Prob. 65CR Ch. 3.CR - 66. The table shows the recommended dosage of...Ch. 3.CR - Prob. 67CR Ch. 3.CR - Prob. 68CR Ch. 3.CR - Whales Diving The figure on the next page, already...Ch. 3.CR - Body Mass Index The following graph shows how the...Ch. 3.CR - Prob. 71CR Ch. 3.CR - Prob. 72CR Ch. 3.CR - Prob. 73CR Ch. 3.CR - Prob. 74CR Ch. 3.EA - A 500-mg dose of a drug is administered by rapid...Ch. 3.EA - A drug is given to a patient by IV infusion at a...Ch. 3.EA - Prob. 3EA Ch. 3.EA - Use the table feature on a graphing calculator or...Ch. 3.EA - 5. Use the table feature on a graphing calculator...Ch. 3.EA - Prob. 6EA

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