Explanation Given: The function is f ( x ) = 4 x − 1 − 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 ) = 4 x − 1 − x 2 x …..(1) Since, the given function is a non-linear function and to obtain the graph of the function at least three points are required. x f ( x ) 1 2 2 3 2 3 2 3 Table 1 Table 1 represents the points 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 ) = 4 x − 1 − x 2 x . From Figure 1 it is observed that as the value of x increases from 0 the value of the function first increases and after some time the value of the function startdecreasing. Since, the curve of the function is concave downwards so, it can be said that in the interval ( 0 , 3 ) there exists a point of maxima for the given function and the point of minima 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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Question

Chapter 4.2, Problem 62E

To determine

To sketch:

The graph of the function f(x)=4x−1−x2x and explain that in the interval (0,3) the maximum value of the function exists and the minimum value does not exist. Also obtain the maximum value of the function.

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Chapter 4.2, Problem 61E

Chapter 4.2, Problem 63E

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Chapter 4 Solutions

Calculus: Early Transcendentals

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The graph of the function f ( x ) = 4 x − 1 − x 2 x and explain that in the interval ( 0 , 3 ) the maximum value of the function exists and the minimum value does not exist. Also obtain the maximum value of the function.

Solution Summary: The author illustrates the graph of the function f(x)=4x-1-x

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To sketch:

The graph of the function f(x)=4x−1−x2x and explain that in the interval (0,3) the maximum value of the function exists and the minimum value does not exist. Also obtain the maximum value of the function.

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Chapter 4 Solutions

The graph of the function f ( x ) = 4 x − 1 − x 2 x and explain that in the interval ( 0 , 3 ) the maximum value of the function exists and the minimum value does not exist. Also obtain the maximum value of the function.

Solution Summary: The author illustrates the graph of the function f(x)=4x-1-x

Concept explainers

Videos

To sketch: The graph of the function f(x)=4x−1−x2x and explain that in the interval (0,3) the maximum value of the function exists and the minimum value does not exist. Also obtain the maximum value of the function.

Want to see the full answer?

Chapter 4 Solutions

To sketch:

The graph of the function f(x)=4x−1−x2x and explain that in the interval (0,3) the maximum value of the function exists and the minimum value does not exist. Also obtain the maximum value of the function.