Explanation Given: One of the slope fields in Figures (A) and (B) is the slope field for d y d t = t 2 . The other is d y d t = y 2 Calculation: In the case of d y d t = t 2 , the slope depends only on t . The isoclines of any slope c will consist of two vertical lines t = ± c . This indicates that the slope field will be the one given in Figure (A). Similarly, in the case of d y d t = y 2 , the slope depends only on y . The isoclines of any slope c will consist of two horizontal lines y = ± c . This indicates that the slope field will be the one given in Figure (B)

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ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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Chapter 9.3, Problem 4E

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To identify which slope field matches which figure and sketch the solutions with initial conditions y(0)=1, y(0)=0 and y(0)=−1.

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Chapter 9.3, Problem 3E

Chapter 9.3, Problem 5E

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2. (5 points) Let f(x) = = - - - x² − 3x+7. Find the local minimum and maximum point(s) of f(x), and write them in the form (a, b), specifying whether each point is a minimum or maximum. Coordinates should be kept in fractions. Additionally, provide in your answer if f(x) has an absolute minimum or maximum over its entire domain with their corresponding values. Otherwise, state that there is no absolute maximum or minimum. As a reminder, ∞ and -∞ are not considered absolute maxima and minima respectively.

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EBK CALCULUS: EARLY TRANSCENDENTALS

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To identify which slope field matches which figure and sketch the solutions with initial conditions y ( 0 ) = 1 , y ( 0 ) = 0 and y ( 0 ) = − 1 .

Solution Summary: The author identifies which slope field matches which figure and sketched the solutions with initial conditions y(0)=1.

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To identify which slope field matches which figure and sketch the solutions with initial conditions y(0)=1, y(0)=0 and y(0)=−1.

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Chapter 9 Solutions