Explanation Given: The function is given as: f ( x ) = x − ln | x | Graph: To obtain the plot, the steps to be followed are: Step 1: In the TI-83 graphical calculator, press the Y = key. Step 2: Enter the equation of f ( x ) as X − ln | X | in Y 1 . Step 3: Press the TRACE and Y key. Step 4: Go to WINDOW and set X min = − 6 X max =6Y min = − 6 Y max =6 . Step5: Click on the TRACE key to obtain the graph. The graph is obtained as follows: To obtain y -intercept, put x = 0 . f ( 0 ) = 0 − ln ( 0 ) f ( 0 ) = 0 To find the x -intercept, solve f ( x ) = 0 . x − ln | x | = 0 x = ln | x | Power rule of differentiation states that if f ( x ) = x n for any number n , then f ′ ( x ) = n x n − 1 . Subtraction rule of differentiation states that if: f ( x ) = u ( x ) − v ( x ) Then, f ′ ( x ) is given by f ′ ( x ) = u ′ ( x ) − v ′ ( x ) To find all the critical points, calculate the first-order derivative of the given function. Use power rule and subtraction rule: f ′ ( x ) = d f ( x ) d x = d ( x ) d x − d ( ln | x | ) d x = 1 − 1 x Now put f ′ ( x ) = 0 to find critical points: 1 − 1 x = 0 x = 1 Now f

Mathematics with Applications and Mylab Math with Pearson EText -- Title-Specific Access Card Package

12th Edition

ISBN: 9780134862668

Author: Lial, Margaret L.

Publisher: Pearson Education Canada

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Chapter 12.6, Problem 19E

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To graph: The function f(x)=x−ln|x| and locate the point of inflection and local extrema.

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Chapter 12.6, Problem 18E

Chapter 12.6, Problem 20E

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Mathematics with Applications and Mylab Math with Pearson EText -- Title-Specific Access Card Package

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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To graph: The function f ( x ) = x − ln | x | and locate the point of inflection and local extrema.

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To graph: The function f(x)=x−ln|x| and locate the point of inflection and local extrema.

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Chapter 12 Solutions