To determine To calculate: The intervals where the given function f ( x ) = 2 x − 4 is concave upward or concave downward along with any inflection point. Explanation Given: The function is f ( x ) = 2 x − 4 . Formula used: Let f ( x ) be a function whose first and second derivatives exist at all points in the interval (a, b). 1. If f ″ ( x ) > 0 for all x in (a, b), then f ( x ) is concave upward on (a, b). 2. If f ′ ′ ( x ) < 0 for all x in (a, b), then f ( x ) is concave downward on (a, b) Calculation: The condition for the function to be concave upward is: f ″ ( x ) > 0 The condition for the function to be concave downward is: f ″ ( x ) < 0 Write the given function. f ( x ) = 2 x − 4 …… (1) Do first derivative of the function. f ′ ( x ) = ( x − 4 ) ( 0 ) − 2 ( 1 − 0 ) ( x − 4 ) 2 = − 2 ( x − 4 ) 2 Do second derivative of the function

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 29E

To determine

To calculate: The intervals where the given function f(x)=2x−4 is concave upward or concave downward along with any inflection point.

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Chapter 12.2, Problem 28E

Chapter 12.2, Problem 30E

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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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