Explanation Given information: The function is as, f ( x ) = 2 x − x Graph: Consider Y 1 as the function f ( x ) . Y 1 = f ( x ) Substitute 2 x − x for f ( x ) in the function Y 1 = f ( x ) as follows, Y 1 = 2 x − x To obtain graph of the function f ( x ) = 2 x − x , first turn ON the calculator and press Y= button then insert the equation Y 1 = 2 x − x as shown in Figure 1. Press the WINDOW button and set the viewing window as shown in Figure 2. After this press the GRAPH button and the graph is obtained as shown in Figure 3. From Figure 3 it can be seen that the graph of the function f ( x ) = 2 x − x has the maxima and there is no minima of the graph in the viewing window [ 0 , 4 ] by [ 0 , 2 ] . To obtain the maximum of the function f ( x ) = 2 x − x press 2 nd TRACE and choose option 4 as shown in Figure 4. To obtain the maxima of the function f ( x ) = 2 x − x , first choose the Left bound that is slightly left to the maximum point as shown in Figure 5. Then choose Right bound that is slightly right to the maximum point as shown in Figure 6. Guess the point nearer to the maximum of the function f ( x ) = 2 x − x as shown in Figure 7. Press ENTER to obtain the maximum of the function f ( x ) = 2 x − x as shown in Figure 8. The y -coordinate of the point ( 1 , 1 ) gives the maximum value of the function f ( x ) = 2 x − x . Thus, the maximum value of the function f ( x ) = 2 x − x is 1 . Calculation: To obtain the maximum value of the function f ( x ) = 2 x − x , differentiate the function f ( x ) with respect to x . d d x f ( x ) = d d x ( 2 x − x ) f ′ ( x ) = 2 ( 1 2 x ) − 1 f ′ ( x ) = 1 x − 1 To obtain the critical point of the function, equate the derivative of the function f ( x ) = 2 x − x with 0

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 4.2, Problem 21E

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The function f(x)=2x−x on the interval [0,4] and find maximum value.

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Chapter 4.2, Problem 20E

Chapter 4.2, Problem 22E

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Chapter 4 Solutions

Calculus - Standalone book

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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To graph: The function f ( x ) = 2 x − x on the interval [ 0 , 4 ] and find maximum value.

Solution Summary: The author explains how to obtain graph of the function f(x)=2sqrtx-x.

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To graph:

The function f(x)=2x−x on the interval [0,4] and find maximum value.

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Chapter 4 Solutions

To graph: The function f ( x ) = 2 x − x on the interval [ 0 , 4 ] and find maximum value.

Solution Summary: The author explains how to obtain graph of the function f(x)=2sqrtx-x.

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To graph: The function f(x)=2x−x on the interval [0,4] and find maximum value.

Want to see the full answer?

Chapter 4 Solutions

To graph:

The function f(x)=2x−x on the interval [0,4] and find maximum value.