Explanation Given: i. f ′ ( x ) < 0 for x < 0 and f ″ ( x ) > 0 for x > 0 , and ii. f ″ ( x ) < 0 for | x | > 2 and f ″ ( x ) > 0 for | x | < 2 . Formula used: Test for concavity: Let f ″ ( x ) exist for all x ∈ ( a , b ) , then · y = f ″ ( x ) > 0 for all x ∈ ( a , b ) , here the function f is concave upward on ( a , b ) . · y = f ″ ( x ) < 0 for all x ∈ ( a , b ) , here the function f is concave downward on ( a , b ) . y = f ( x ) has a point of inflection if f ″ ( x ) = 0

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Differential Equations

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Chapter 4.4, Problem 56E

To determine

Draw the graph of a function f that satisfy the given conditions.

i. f′(x)<0 for x<0 and f″(x)>0 for x>0, and

ii. f″(x)<0 for |x|>2 and f″(x)>0 for |x|<2.

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Chapter 4.4, Problem 55E

Chapter 4.4, Problem 57E

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17. Consider a mass-spring system that satisfies 2y′′(t) + by′(t) + 50y(t) = 0.Which of the following is/are true?(i) If b = 0, the motion is critically damped with period π/5 .(ii) If b = 12, the motion is underdamped.(iii) If b = 40, the motion is overdamped.A. (ii) and (iii) only B. (ii) only C. (i) and (ii) only D. (i) and (iii) only E. All

20. Find the general solution to the differential equation y(4) − 8y′′ + 16y = 0A. y = c1e^2x + c2e^−2xB. y = c1xe^2x + c2xe^−2xC. y = c1e^2x + c2e^−2x + c3xe^2x + c4xe^−2xD. y = c1xe^2x + c2xe^−2x + c3x^2e^2x + c4x^2e^−2xE. y = c1 cos 2x + c2 sin 2x + c3x cos 2x + c4x sin 2x

9. A 1 kg mass is attached to a spring with constant 13 N/m. The system is immersed in amedium which offers a damping force numerically equal to 6 times the instantaneous velocity.If x is the displacement of the mass from equilibrium, measured in meters,then x′′ + 6x′ + 13x = 0 . Which of the following statements is true?A. x(t) = c1e^−t + c2e^−5t, and the system is underdamped.B. x(t) = c1e^−t + c2e^−5t, and the system is overdamped.C. x(t) = c1e^−3t cos(2t) + c2e^−3t sin(2t), and the system is underdamped.D. x(t) = c1e^−3t cos(2t) + c2e^−3t sin(2t), and the system is overdamped.

Chapter 4 Solutions

CALCULUS (CLOTH)

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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Draw the graph of a function f that satisfy the given conditions. i. f ′ ( x ) < 0 for x < 0 and f ″ ( x ) > 0 for x > 0 , and ii. f ″ ( x ) < 0 for | x | > 2 and f ″ ( x ) > 0 for | x | < 2 .

Solution Summary: The author explains how to draw the graph of a function f that satisfy the given conditions.

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Draw the graph of a function f that satisfy the given conditions.

i. f′(x)<0 for x<0 and f″(x)>0 for x>0, and

ii. f″(x)<0 for |x|>2 and f″(x)>0 for |x|<2.

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Chapter 4 Solutions

Draw the graph of a function f that satisfy the given conditions. i. f ′ ( x ) &lt; 0 for x &lt; 0 and f ″ ( x ) &gt; 0 for x &gt; 0 , and ii. f ″ ( x ) &lt; 0 for | x | &gt; 2 and f ″ ( x ) &gt; 0 for | x | &lt; 2 .

Solution Summary: The author explains how to draw the graph of a function f that satisfy the given conditions.

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Draw the graph of a function f that satisfy the given conditions. i. f′(x)<0 for x<0 and f″(x)>0 for x>0, and ii. f″(x)<0 for |x|>2 and f″(x)>0 for |x|<2.

Want to see the full answer?

Chapter 4 Solutions

Draw the graph of a function f that satisfy the given conditions. i. f ′ ( x ) < 0 for x < 0 and f ″ ( x ) > 0 for x > 0 , and ii. f ″ ( x ) < 0 for | x | > 2 and f ″ ( x ) > 0 for | x | < 2 .

Draw the graph of a function f that satisfy the given conditions.

i. f′(x)<0 for x<0 and f″(x)>0 for x>0, and

ii. f″(x)<0 for |x|>2 and f″(x)>0 for |x|<2.