To determine To calculate: f ″ ( x ) , f ″ ( 0 ) , f ″ ( 2 ) and f ″ ( − 3 ) , for the given function f ( x ) = ln ( 2 x + 1 ) Explanation Given: The function is f ( x ) = ln ( 2 x + 1 ) . Formula used: If the given function is f ( x ) , then f ′ ( x ) represents the first derivative of the function f ( x ) . Similarly, the derivative f ″ ( x ) of the function f ′ ( x ) represents the second derivative of the given function f ( x ) . and If f ( x ) = ln x , then f ′ = d d x ( ln x ) x Calculation: The function is given as f ( x ) = ln ( 2 x + 1 ) . Find the first derivative of the function. f ′ ( x ) = d d x ( ln ( 2 x + 1 ) ) = 1 2 x + 1 ⋅ d d x ( 2 x + 1 ) = 1 2 x + 1 ( 2 ( 1 ) + 0 ) = 2 2 x + 1 Now, find the second derivative of the function. f ′ ′ ( x ) = d d x ( f ′ ( x ) ) = d d x ( 2 2 x + 1 ) = ( 2 x + 1 ) d d x ( 2 ) − 2 d d x </

Mathematics With Applications, Loose-leaf Edition Plus Mylab Math With Pearson Etext -- 18-week Access Card Package (12th Edition)

12th Edition

ISBN: 9780135998304

Author: Margaret L. Lial, Tom Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

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Chapter 12.2, Problem 13E

To determine

To calculate: f″(x),f″(0),f″(2) and f″(−3), for the given function f(x)=ln(2x+1)

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Chapter 12.2, Problem 6E

Chapter 12.2, Problem 14E

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Chapter 12 Solutions

Mathematics With Applications, Loose-leaf Edition Plus Mylab Math With Pearson Etext -- 18-week Access Card Package (12th Edition)

Ch. 12.1 - Checkpoint 1 For what values of x is the function...Ch. 12.1 - Checkpoint 2 Find all intervals on which is...Ch. 12.1 - Checkpoint 3 Identity the x-values of all points...Ch. 12.1 - Checkpoint 4 Find the critical numbers for each of...Ch. 12.1 - Prob. 5CP Ch. 12.1 - Prob. 6CP Ch. 12.1 - Checkpoint 7 Find the locations of the local...Ch. 12.1 - Prob. 8CP Ch. 12.1 - Checkpoint 9 If a sales function is given by...Ch. 12.1 - Prob. 1E

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