/*! 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. 83 Determine the local extrema of t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q. 83 (page 311)

Determine the local extrema of the function,

f(x)=x3e-x,I=[0,鈭�),J=(-鈭�,鈭�).

Short Answer

Expert verified

The value

Step by step solution

01

Step 1. Given Information.

The function is,

f(x)=x3e-x,I=[0,鈭�),J=(-鈭�,鈭�).

02

Step 2. The critical point.

For critical points we consider,

f'(x)=0ddx(x3e-x)=0x3(-e-x)+(e-x)3x2=0x2e-x(-x+3)=0

Dividing both sides by e-x,

x2(-x+3)=0

Either x=0

or, role="math" localid="1648585031235" -x+3=0鈬�x=3

Hence,x=0,3.

03

Step 3. Values of I.

Now,

limx鈫�0f(x)=limx鈫�0x3e-x=0

localid="1648585483256">limx鈫�鈭�f(x)=limx鈫�鈭�x3e-x=limx鈫�鈭�x3ex[鈭�鈭�]=limx鈫�鈭�6xex=limx鈫�鈭�6ex=6鈭�=0

The graph of the function with limit I=(0,鈭�)is shown as,

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

For each set of sign charts in Exercises 53鈥�62, sketch a possible graph of f.

Find the critical points of the function

f'(x)=(x-1)(x-2)x-3

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)=(x-1)2x+2

Find the possibility graph of its derivative f'.

Restate Theorem 3.3 so that its conclusion has to do with

tangent lines.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

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.