/*! 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. 22 If possible, find constants a an... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q. 22 (page 197)

If possible, find constants a and b so that the function f that follows is continuous and differentiable everywhere. If it is not possible, explain why not.

f(x)=ax-b,ifx<2bx2+1,ifx鈮�2

Short Answer

Expert verified

Ans:b=15&a=45

Step by step solution

01

Step 1. Given information is:

f(x)=ax-b,ifx<2bx2+1,ifx鈮�2

02

Step 2. Calculating a and b

Differentiatingthefunction,f'(x)=a,ifx<22bx,ifx鈮�2Sinceitiscontinuousanddifferentiablethereforelefthandderivativeatx=2,isaandrighthandderivativeatx=2isf'(2)=4b.Therefore,a=4b.....(1)Nowthefunctioniscontinuousatx=2Therefore,limx鈫�2-ax+b=limx鈫�2+bx2+12a+b=4b+12(4b)+b=4b+1[From(1)]5b=1b=15Putvalueofbin(1)a=45

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, in two ways, that the power rule holds for negative integer powers

a) by using the z鈫�xdefinition of the derivative

b) by using theh鈫�0definition of the derivative

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)=(x+1)(3x-4)x3-27

State the chain rule for differentiating a composition g(h(x))of two functions expressed

(a) in 鈥減rime鈥� notation and

(b) in Leibniz notation.

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)=x2-x3+5x9x-1

For each function f that follows find all the x-values in the domain of f for which f'(x)=0and all the values for which f'(x)does not exist in later section we will call these values the critical points of f

localid="1648604345877" a)f(x)=x3-2xb)f(x)=x-xc)鈥�f(x)=11+xd)f(x)=x2(x-1)(x-2)2
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

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.