   Chapter 3.3, Problem 26E

Chapter
Section
Textbook Problem

# 20-27 Sketch the graph of a function that satisfies all of the given conditions. f ′ ( 0 ) = f ′ ( 4 ) = 0 ,   f ′ ( x ) = 1  if  x < − 1 , f ′ ( x > ) > 0  if  0 < x < 2 , f ′ ( x ) < 0  if  − 1 < x < 0  or 2 < x < 4  or  x > 4 , lim x → 2 − f ′ ( x ) = ∞ ,   lim x → 2 + f ′ ( x ) = − ∞ f ′ ′ ( x ) > 0  if  − 1 < x < 2  or 2 < x < 4 , f ′ ′ ( x ) < 0  if  x > 4

To determine

To sketch:

The graph satisfying the given conditions

Explanation

1) Concept:

i. Increasing or Decreasing test:

If f'x>0 then f is increasing

If f'x<0 then f is decreasing

ii. Concavity test:

If f"(x)>0 then the graph of f is concave upward

If f"(x)<0 then the graph of f is concave downward

2) Given:

f'0=f'4=0,

f'x=1 if x<-1

f'x>0 if 0<x<2

f'x<0 if-1<x<0 or 2<x<4 or x>4

limx2-f'x= and limx2+f'x=-

f"(x)>0 if -1<x<2 or 2<x<4

f"(x)<0 if x>4

3) Calculation:

f'0=f'4</

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Sketch the graphs of the equations in Exercises 512. yx=1

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Exercises 4144, determine whether the statement is true or false. 43. 2356

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### What are the five steps of the scientific method?

Research Methods for the Behavioral Sciences (MindTap Course List) 