/*! 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 29 Finda function f聽that has the g... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q 29 (page 238)

Find

a function fthat has the given derivative f' and value f(c).

f'x=x3x+1,f2=4

Short Answer

Expert verified

Antiderivative isf(x)=x3+x22-6

Step by step solution

01

Step 1:Given information

The given expression isf'x=x3x+1,f2=4

02

Step 2:Simplification

given

f'x=x3x+1=3x2+x

We will use an intelligent guess-and-check method to find f

Here 3x2is derivative of x3and x is derivative of x22

hence,

f(x)=x3+x22+c

Now,f(2)=4

鈬�4=23+222+c

鈬�4=8+2+c鈬�c=-6

Therefore

f(x)=x3+x22-6

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 function graphed 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.

If Katie walked at 3miles per hour for 20minutes and then sprinted at 10miles an hour for 8minutes, how fast would Dave have to walk or run to go the same distance as Katie did at the same time while moving at a constant speed? Sketch a graph of Katie鈥檚 position over time and a graph of Dave鈥檚 position over time on the same set of axes.

Use (a) the h鈫�0definition of the derivative and then

(b) the z鈫�cdefinition of the derivative to find f'(c) for each function f and value x=c in Exercises 23鈥�38.

29.f(x)=x12,x=9

Use the definition of the derivative to find ffor each function fin Exercises 39-54.

f(x)=x2-1x2-x-2

Suppose f is a polynomial of degree n and let k be some integer with 0鈮�k鈮�n. Prove that if f(x) is of the form f(x)=anxn+an-1xn-1+....+a1x+a0

Then ak=fk(0)k!where fk(x)is the k-th derivative off(x)andk!=k路(k-1)路(k-2)....2路1
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure 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.