/*! 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. 30 In Problems 21鈥�32, find the de... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Q. 30 (page 897)

In Problems 21鈥�32, find the derivative of each function at the given number.

f(x)=x3-2x2+xat-1

Short Answer

Expert verified

The derivative of the given function at -1is equal to8

Step by step solution

01

Step 1. Given information

Given function is f(x)=x3-2x2+x

We have to find the derivative of the given function at-1

02

Step 2. Definition of the derivative

Let's say a function

The derivative of the function at is defined as

f'(c)=limx鈫�cf(x)-f(c)x-c

03

Step 3. Finding the derivative

By substituting the given function in the derivative definition,

we will get:

f'(-1)=limx鈫�-1f(x)-f(-1)x-(-1)鈬�f'(-1)=limx鈫�-1(x3-2x2+x)-((-1)3-2(-1)2-1)x+1鈬�f'(-1)=limx鈫�-1(x3-2x2+x)+4x+1

04

Step 4. Simplifying the limit

By rewriting the limit, we will have:

f'(-1)=limx鈫�-1x3-2x2+x+4x+1鈬�f'(-1)=limx鈫�-1(x+1)(x2-3x+4)x+1鈬�f'(-1)=limx鈫�-1(x2-3x+4)鈬�f'(-1)=(-1)2-3(-1)+4鈬�f'(-1)=8

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

Find limit algebraically:limx鈫�-32x3

In Problems 13鈥�32, use the accompanying graph of y=f(x).

What is the domain of f?

In Problems 7鈥�16, use a table to find the indicated limit.

10.limx鈫�02-xx2+4.

Graph each function. Use the graph to find the indicated limit, if it exists.

limx鈫�-1f(x),f(x)=2x-1

In Problems 7鈥� 42, find each limit algebraically.

limx鈫�23x+4x2+x.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

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.