   Chapter 4.7, Problem 22E

Chapter
Section
Textbook Problem

Find the point on the curve y = x that is closest to the point (3, 0).

To determine

To find: The point on the curve y=x that is closest to the point (3,0).

Explanation

Formula used:

Distance from the point (x,y) to (x1,y1) is D=(xx1)2+(yy1)2

Calculation:

Let (x,y) be a point on the curve y=x.

Distance from the point (x,y) to (3,0) is,

D=(x3)2+(y0)2=(x3)2+(x)2=x25x+9

Differentiate D with respect to x,

dDdx=121x25x+9(2x5)=122x5x25x+9

For critical points, set dDdx=0 and solve for x.

122x5x25x+9=02x5=0x=52

Differentiate dDdx with respect x,

d2D

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Convert the expressions in Exercises 6584 to power form. 23x1.2x2.13

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 2934, rationalize the denominator of each expression. 34. 2a+b2ab

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Find each product: (a+5)(a5)

Elementary Technical Mathematics

True or False: By the Integral Test, converges.

Study Guide for Stewart's Multivariable Calculus, 8th

The arc length of y = 3x + 2 from x = 1 to x = 5 is a) 210 b) 52 c) 102 d) 410

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