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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem
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The number of bacteria after t hours in a controlled laboratory experiment is n = f ( t ) .

(a) What is the meaning of the derivative f ( 5 ) ? What are its units?

(b) Suppose there is an unlimited amount of space and nutrients for the bacteria. Which do you think is larger, f ( 5 ) or f ( 10 ) ? If the supply of nutrients is limited, would that affect your conclusion? Explain.

To determine

(a) To Explain: The meaning of the derivative at 5, f(5) and its unit.

Explanation

The derivative of a function f(x) at a point a is the rate of change of function with respect to change in x when x=a.So The value  f(5)  gives the rate of change of number of bacteria in the laboratory with respect to time at 5 hours.

Also, f (5) is the approximate growth in the number of bacteria between the 5th and 6th hours

To determine

(b) To check: If f (5)is larger than f(10) or vice versa.

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