Chapter 2: Q. 4 (page 119)

Let $P = (x, y)$ be a point on the graph of $y = \frac{1}{x}$
(a) Express the distance $d$ from $p$ to the origin as a function of $x$ .
(b) Use a graphing utility to graph $d = d (x)$ .
(c) For what values of $x$ is $d$ smallest?

Short Answer

Expert verified

The distance $d$ is $d = \sqrt{x^{2} + \frac{1}{x^{2}}}$ and the graph is

and the least value of $d$ is $x = - 1, x = 1$

Step by step solution

Part (a) Step 1: Given information

Given the point $P (x, y)$ and the curve $y = \frac{1}{x}$

Part (a) Step 2: Calculating the distance, we get

Calculating, we get

$d = \sqrt{(x - 0)^{2} + (y - 0)^{2}} d = \sqrt{x^{2} + y^{2}} d (x) = \sqrt{x^{2} + {(\frac{1}{x})}^{2}} d (x) = = \sqrt{x^{2} + \frac{1}{x^{2}}}$

Part (b) Step 1: Given information

Given the equation $d (x) = \sqrt{x^{2} + \frac{1}{x^{2}}}$

Part (b) Step 2: Sketching the graph

Sketching the graph, we get

Part (c) Step 1: Given information

Given the equation $d (x) = \sqrt{x^{2} + \frac{1}{x^{2}}}$

Part (c) Step 2: Checking from the graph

Checking, we get that $d$ is smallest when $x = - 1, x = 1$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Let $P = (x, y)$ be a point on the graph of $y = \frac{1}{x}$
(a) Express the distance $d$ from $p$ to the origin as a function of $x$ .
(b) Use a graphing utility to graph $d = d (x)$ .
(c) For what values of $x$ is $d$ smallest?

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Calculating the distance, we get

Part (b) Step 1: Given information

Part (b) Step 2: Sketching the graph

Part (c) Step 1: Given information

Part (c) Step 2: Checking from the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Geometry

Discrete Mathematics

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Let P=(x,y)be a point on the graph of y=1x(a) Express the distance dfrom pto the origin as a function of x.(b) Use a graphing utility to graph d=d(x).(c) For what values of xis dsmallest?

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Calculating the distance, we get

Part (b) Step 1: Given information

Part (b) Step 2: Sketching the graph

Part (c) Step 1: Given information

Part (c) Step 2: Checking from the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Geometry

Discrete Mathematics

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Let $P = (x, y)$ be a point on the graph of $y = \frac{1}{x}$
(a) Express the distance $d$ from $p$ to the origin as a function of $x$ .
(b) Use a graphing utility to graph $d = d (x)$ .
(c) For what values of $x$ is $d$ smallest?