Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 3.1, Problem 26E

(a)

To determine

To find: the graph of the derivative of the function.

(a)

Expert Solution

Answer to Problem 26E

The graph of the required function is shown below.

Explanation of Solution

Given:

The given graph of the given function is shown below,

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 3.1, Problem 26E , additional homework tip 1

Find the slope of the function between (−4,0) and (0,2) .

m1=2−00−(−4)=24=12

Find the slope of the function between (0,2) and (1,−2) .

m2=−2−21−0=−41=−4

Find the slope of the function between (1,−2) and (4,−2) .

m3=4−1−2−(−2)=3−2+2=0

Find the slope of the function between (4,−2) and (6,2) .

m4=2−(−2)6−4=42=2

So, the function can be written as,

f'(x)={12 −4<x<0−4 0<x<10 1<x<42 4<x<6

So, the graph of the above function is shown below.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 3.1, Problem 26E , additional homework tip 2

Therefore, the graph of the required function is shown above.

(b)

To determine

To find: the value between x=−4 and x=6 of the function at which function is not differentiable.

(b)

Expert Solution

Answer to Problem 26E

The function is not differentiable at the points x=0, 1, 4 .

Explanation of Solution

Given:

The general equation is y=(x−a)(x+b) .

Consider the function.

f'(x)={12 −4<x<0−4 0<x<10 1<x<42 4<x<6

As it clear from the function that at the points x=0, 1, 4 , the left-hand side derivative are different from the right hand side derivative.

So, the function is not differentiable at the points x=0, 1, 4 .

Therefore, the function is not differentiable at the points x=0, 1, 4 .

Chapter 3.1, Problem 25E

Chapter 3.1, Problem 27E

Chapter 3 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 3.1 - Prob. 1QR Ch. 3.1 - Prob. 2QR Ch. 3.1 - Prob. 3QR Ch. 3.1 - Prob. 4QR Ch. 3.1 - Prob. 5QR Ch. 3.1 - Prob. 6QR Ch. 3.1 - Prob. 7QR Ch. 3.1 - Prob. 8QR Ch. 3.1 - Prob. 9QR Ch. 3.1 - Prob. 10QR

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.2 - Prob. 1QR Ch. 3.2 - Prob. 2QR Ch. 3.2 - Prob. 3QR Ch. 3.2 - Prob. 4QR Ch. 3.2 - Prob. 5QR Ch. 3.2 - 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