   Chapter 4.7, Problem 5E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# What is the maximum vertical distance between the line y = x + 2 and the parabola y = x2 for −1 ≤ x ≤ 2?

To determine

To find: The maximum vertical distance between the line y=x+2 and the parabola y=x2 for 1x2 .

Explanation

Given:

The line, y=x+2 (1)

The parabola, y=x2 (2)

Calculation:

The vertical difference between the given two graphs is obtained by subtracting equation (2) from equation (1).

The vertical difference between the graphs y=x+2 and y=x2 , is denoted by S,

S=x+2x2

Use the online graphing calculator to draw the graph of the functions as shown below in Figure 1,

Differentiate S with respect to x,

dSdx=12x

For critical points, dSdx=0 ,

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 