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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 5.5, Problem 13E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Think About It In Exercises 13 and 14, determine which value best approximates the area of the region bounded by the graphs of f and g. Make your selection based on a sketch of the region and not by performing any calculations.

f ( x ) = x + 1 , g ( x ) = ( x − 1 ) 2

(a) -2 (b) 2 (c) 10 (d) 4 (e) 8

To determine

To calculate: The area of the region bounded by the graphs of f(x)=x+1 and g(x)=(x−1)2 by sketching the region only and also match with the provided option for area.

Explanation

Given Information:

Two functions f(x)=x+1 and g(x)=(x−1)2, provided option for the area is as follows:

(a)−2  (b)2  (c)10   (d)4   (e)8

Calculation:

Consider the provided functions,

f(x)=x+1

And, g(x)=(x−1)2

Consider the first function f(x)=x+1

It is a linear function. So, its graph will be a straight line with slope m=1 and y-intercept b=1

Consider the second function g(x)=(x−1)2

It is a quadratic function. So, its graph will be a parabola with opening upwards.

The x-intercept is x=1.

Compute the points of intersection of two graphs by setting the functions equal to each other and solving for x,

f(x)=g(x)x+1=(x−1)2x+1=x2−2x+1x2−3x=0

Factor the above polynomial,

x(x−3)=0

Apply zero product property,

<

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