Chapter 11.1, Problem 28ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# In 27 and 28, functions f and g are defined. In each case sketch the graphs of f and 2g on the same set of axes and find a number x 0 so that f ( x ) ≤ 2 g ( x ) for all x > x 0 . You can find an exact value for x 0 by solving a quadratic equation, or you can find an approximate value for x 0 by using a graphing calculator or computer. 28. f ( x ) = x 2 + 125 x + 254 and g ( x ) = x 2 for each real number x ≥ 0

To determine

To show:

Determine the approximate value.

f(x)=x2+125x+254andg(x)=x2 for all real numbers x0

Explanation

Given information:

Consider the functions.

f(x)=x2+125x+254andg(x)=x2

for all real numbers x0

the objective is to draw the graphs of f and 2g on the same set of axes.

Concept used:

Draw the graph of f and 2g on the same set of  axes.

Calculation:

Consider the functions.

f(x)=x2+125x+254andg(x)=x2

for all real numbers x0

the objective is to draw the graphs of f and 2g on the same set of axes.

Objective is to find an exact value for x0 by solving a quadratic equation.

To find the answer algebraically, solve the equation 2x2=x2+125x+254.

Subtract x2 from both sides gives x2125x254=0 and then take factor

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