Explanation Given Information: The provided function is: f ( x ) = e x − x 4 4 Graph: Consider the provided function: f ( x ) = e x − x 4 4 Now, differentiate the provided function with respect to x as: f ′ ( x ) = d d x ( e x − x 4 4 ) = e x − x 3 Now, plot this graph using TI-83 as: Step1: Press ON key. Step2: Press “Y=” key. Step3: Enter the equation “ e ^ ( X ) − X ^ ( 3 ) ” before Y 1 . Step4: Press WINDOW key and set Xmin as − 6 , Xmax as 6 and Ymax as 15 . Step5: Press GRAPH key. The graph so obtained is depicted below: Now, as it can be observed from the graph that y = 0 or f ' ( x ) = 0 for x ≈ 1.86 , x ≈ 4.54 . Now, to find the minima, substitute 1.86 for x in the provided function as, f ( 1.86 ) = e ( 1.86 ) − ( 1.86 ) 4 4 = 3.43 Thus, the function has relative maximum at ( 1.86 , 3.43 ) . Also, substitute 4.54 for x in the provided function as, f ( 4.54 ) = e ( 4.54 ) − ( 4.54 ) 4 4 = − 12.52 Thus, f ( x ) has relative minimum at ( 4.54 , − 12.52 ) . Now, obtain f ″ ( x ) as: f ″ ( x ) = d d x ( e x − x 3 ) = e x − 3 x 2 Now, plot this graph using TI-83 as: Step1: Press ON key. Step2: Press “Y=” key. Step3: Enter the equation “ e ^ ( X ) − 3 × X ^ ( 2 ) ” before Y 1

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 12.4, Problem 30E

To determine

To graph: The function f(x)=ex−x44 and label point of inflection and all the relative and absolute extrema and vertical and horizontal asymptotes.

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Chapter 12.4, Problem 29E

Chapter 12.4, Problem 31E

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Finite Mathematics and Applied Calculus (MindTap Course List)

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To graph: The function f ( x ) = e x − x 4 4 and label point of inflection and all the relative and absolute extrema and vertical and horizontal asymptotes.

Solution Summary: The author illustrates the graph using TI-83. The provided function is f(x)=ex-

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To graph: The function f(x)=ex−x44 and label point of inflection and all the relative and absolute extrema and vertical and horizontal asymptotes.

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Chapter 12 Solutions