Explanation Given: The function is f ( x ) = 4 x − 2 x + 3 . 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 − 2 x + 3 …..(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 ) 0 3 1 5 3 3.928 Table 1 Table 1 represents the points that lie 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 − 2 x + 3 . From Figure 1 it is observed that as the value of x increases from 0 the value of the function first increases and as the value of x reaches 1 the value of function starts decreasing continuously. From the Figure 1 it is observed that the point of minima occurs at x = 0 and the point of maxima occurs at x = 1 . Critical points are the points at which the value of f ′ ( x ) is zero or f ′ ( x ) does not exists. To obtain the critical points differentiate equation (1) as shown below: f ′ ( x ) = d ( 4 x − 2 x + 3 ) d x = ( ( 4 ⋅ 1 2 x ) − 2 ) = 2 x − 2 = 2 − 2 x x To obtain the critical points for the given function f ( x ) solve the equation f ′ ( x ) = 0 as shown below: f ′ ( x ) = 0 To solve the above equation substitute the expression f ′ ( x ) = 2 − 2 x x in the above equation as shown below: f ′ ( x ) = 0 2 − 2 x x = 0 2 − 2 x = 0 x = 2 2 Further solve the above equation

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

Chapter 4.2, Problem 25E

To determine

To sketch:

The graph of the function f(x)=4x−2x+3 and indicate the point of minima and the point of maxima in the interval [0,3]. Also obtain the maximum value and the minimum value of the function.

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Chapter 4.2, Problem 24E

Chapter 4.2, Problem 26E

Chapter 4 Solutions

Calculus: Early Transcendentals

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Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY

The graph of the function f ( x ) = 4 x − 2 x + 3 and indicate the point of minima and the point of maxima in the interval [ 0 , 3 ] . Also obtain the maximum value and the minimum value of the function.

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

Concept explainers

Videos

To sketch:

The graph of the function f(x)=4x−2x+3 and indicate the point of minima and the point of maxima in the interval [0,3]. Also obtain the maximum value and the minimum value of the function.

Want to see the full answer?

Chapter 4 Solutions

The graph of the function f ( x ) = 4 x − 2 x + 3 and indicate the point of minima and the point of maxima in the interval [ 0 , 3 ] . Also obtain the maximum value and the minimum value of the function.

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

Concept explainers

Videos

To sketch: The graph of the function f(x)=4x−2x+3 and indicate the point of minima and the point of maxima in the interval [0,3]. Also obtain the maximum value and the minimum value of the function.

Want to see the full answer?

Chapter 4 Solutions

To sketch:

The graph of the function f(x)=4x−2x+3 and indicate the point of minima and the point of maxima in the interval [0,3]. Also obtain the maximum value and the minimum value of the function.