Explanation Given: The function is f ( x ) = 2 + x 2 x . Concept used: Critical points: For a function f ( x ) critical points are the points at which the value of f ′ ( x ) is zero or f ′ ( x ) does not exists. Calculation: The given function is expressed as follows: f ( x ) = 2 + x 2 x …..(1) Since, the given function is a non-linear function and to obtain the graph of the function three points are required. x f ( x ) 1 3 3 11 3 6 38 6 Table 1 Table 1 represents the points through that lies on the curve of the given function. Plot the points on the Cartesian plane and join the points to obtain the curve of the given function. Figure 1 represents the graph of the function f ( x ) = 2 + x 2 x on the interval ( 0 , 5 ) . From Figure 1 it is observed that as the value of x increases from 0 the value of the function first decreases and after some time the value of the function started increasing. Since, the curve of the function is concave upwards so, it can be said that in the interval ( 0 , 5 ) there exists a point of minima for the given function and the point of maxima does not exists. Critical points are the points at which the value of f ′ ( x ) is zero or f ′ ( x ) does not exists

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 4.2, Problem 61E

To determine

To sketch:

The graph of the function f(x)=2+x2x and explain that in the interval (0,5) the minimum value of the function exists and the maximum value does not exist. Also obtain the minimum value of the function.

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Chapter 4.2, Problem 60E

Chapter 4.2, Problem 62E

Chapter 4 Solutions

Calculus: Early Transcendentals

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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The graph of the function f ( x ) = 2 + x 2 x and explain that in the interval ( 0 , 5 ) the minimum value of the function exists and the maximum value does not exist. Also obtain the minimum value of the function.

Solution Summary: The author illustrates the graph of the function f(x)=2+x

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The graph of the function f(x)=2+x2x and explain that in the interval (0,5) the minimum value of the function exists and the maximum value does not exist. Also obtain the minimum value of the function.

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The graph of the function f ( x ) = 2 + x 2 x and explain that in the interval ( 0 , 5 ) the minimum value of the function exists and the maximum value does not exist. Also obtain the minimum value of the function.

Solution Summary: The author illustrates the graph of the function f(x)=2+x

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To sketch: The graph of the function f(x)=2+x2x and explain that in the interval (0,5) the minimum value of the function exists and the maximum value does not exist. Also obtain the minimum value of the function.

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Chapter 4 Solutions

To sketch:

The graph of the function f(x)=2+x2x and explain that in the interval (0,5) the minimum value of the function exists and the maximum value does not exist. Also obtain the minimum value of the function.