/*! 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. 40 Use the definition of the deriva... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q. 40 (page 184)

Use the definition of the derivative to find f' for each function f.

f(x)=4+x2

Short Answer

Expert verified

f'(x)=2x

Step by step solution

01

Step 1. Given information. 

We have been given a function:

f(x)=4+x2

We have to find f' using the definition of the derivative.

02

Step 2. Find the derivative 

Derivative of the function can be found as :

limh鈫�0鈥�f(x+h)鈭�f(x)h=limh鈫�0鈥�4+(x+h)2鈭�4+x2h=limh鈫�0鈥�4+x2+2xh+h2鈭�4鈭�x2h=limh鈫�0鈥�h(2x+h)h=limh鈫�0鈥�2x+h=2x

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

Prove that if f is any cubic polynomial function f(x)=ax3+bx2+cx+dthen the coefficients of f are completely determined by the values of f(x) and its derivative at x=0 as follows

a=f"'(0)6;b=f"(0)2;c=f'(0);d=f(0)

Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.

The line that passes through the point (3,2)and is parallel to the tangent line to f(x)=1x at x=-1.

Use the definition of the derivative to prove the following special case of the product rule

ddx(x2f(x))=2xf(x)+x2f'(x)

Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=2-3x+1

For each function fgraphed in Exercises 65-68, determine the values of xat which ffails to be continuous and/or differentiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Mechanics 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.