/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 34 find the point on the graph of t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q. 34 (page 288)

find the point on the graph of the function fthat is closest to the point(a,b)by minimizing the square of the distance from the graph to the point.

f(x)=x2+1 and the point (2,0)

Short Answer

Expert verified

Ans: The point is,(1,2)

Step by step solution

01

Step 1. Given information.

given, f(x)=x2+1

and the point is, (2,0)

02

Step 2. The objective is to find a point closest to the function that is closest to the point by minimizing the graph from the distance to the point.

Let, the point be (x,y).

The distance between (2,0)and (x,y)is,

D(x)=(0-y)2+(2-x)2D(x)=y2+4+x2-4xD(x)=(x2+1)2+x2+4-4xD(x)=2x2-4x+5

03

Step 3. Now,

D(x)=2x2-4x+5D'(x)=2x-22x2-4x+5

Again,

D'(x)=0

2x-22x2-4x+5=02x-2=0x=1

04

Step 4.  Putting x=1 in f(x)=x2+1 .

f(x)=2

Therefore, the point is(1,2).

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use the first derivative test to determine the local extrema of each function in Exercises 39- 50. Then verify your algebraic answers with graphs from a calculator or graphing utility.

f(x)=x2(x-1)(x+1)

Use a sign chart for f'to determine the intervals on which each function fis increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.

ln(x2+1)

Sketch careful, labeled graphs of each function f in Exercises 63鈥�82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of f,f',andf'', and examine any relevant limits so that you can describe all key points and behaviors of f.

f(x)=x4-x

Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points.

fx=3x-2ex

Last night at 6 p.m., Linda got up from her blue easy chair. She did not return to her easy chair until she sat down again at 8 p.m. Let s(t) be the distance between Linda and her easy chair t minutes after 6 p.m. last night.

(a) Sketch a possible graph of s(t), and describe what Linda did between 6 p.m. and 8 p.m. according to your graph. (Questions to think about: Will Linda necessarily move in a continuous and differentiable way? What are good ranges for t and s?

(b) Use Rolle鈥檚 Theorem to show that at some point between 6 p.m. and 8 p.m., Linda鈥檚 velocity v(t) with respect to the easy chair was zero. Find such a place on the graph of s(t).
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.