   Chapter 4.7, Problem 43E Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Solutions

Chapter
Section Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

Minimum Distance Sketch the graph of f ( x ) = 2 − 2 sin x on the interval [ 0 , π / 2 ] .(a) Find the distance from the origin to the y-intercept and the distance from the origin to the x-intercept.(b) Write the distance d from the origin to a point on the graph of f as a function of x.(c) Use calculus to find the value of x that minimizes the function d on the interval [ 0 , π / 2 ] . What is the minimum distance? Use a graphing utility to verify your results.(Submitted by Tim Chapell, Penn Valley Community College, Kansas City, MO)

To determine

To graph: The function f(x)=22sinx on the interval [0,π2].

Explanation

Graph:

Set up a table of coordinates to get the graph as:

xf(x)022sin(0)=2π622sinπ6=1π422sinπ4=0

(a)

To determine

To calculate: The distance from the origin to the x and y intercepts for the function f(x)=22sinx.

(b)

To determine
The distance formula from the origin to any point on the graph of the function f(x)=22sinx.

(c)

To determine

To calculate: The value of x that minimizes the distance from any point on the function f(x)=22sinx to the origin and to verify the result using a graphing utility.

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