Explanation Given: i. f ′ ( x ) > 0 for all x ii. f ″ ( x ) < 0 for x < 0 and f ″ ( x ) > 0 for x > 0 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 )

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Differential Equations

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Chapter 4.4, Problem 55E

To determine

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

i. f′(x)>0 for all x

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

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Chapter 4.4, Problem 54E

Chapter 4.4, Problem 56E

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Chapter 4 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

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

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 all x

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

Want to see the full answer?

Chapter 4 Solutions

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

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

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

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

i. f′(x)>0 for all x

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