Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

Sketch the graph of a function that satisfies all of the given conditions

Vertical asymptote $ x = 0 $, $ f'(x) > 0 $ if $ x < -2 $,$ f'(x) < 0 $ if $ x > -2 (x \not= 0) $,$ f"(x) < 0 $ if $ x < 0 $, $ f"(x) > 0 $ if $ x > 0 $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Kian Manafi

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

03:01

Fahad Paryani

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 3

How Derivatives Affect the Shape of a Graph

Derivatives

Differentiation

Volume

Missouri State University

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

04:35

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

06:14

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

01:53

Sketch the graph of a func…

01:04

02:05

02:44

Sketch a graph of a functi…

00:35

Sketch the graph of the fu…

01:30

Okay, so we're given four conditions that are graph has to meet you have this vertical ascent owed at X is equal to zero. We are increasing or are derivative is greater than zero when X is less than negative two were decreasing when X is greater than negative two. And our second derivative is less than zero for X being less than zero. And our second derivative being less than zero means that we are just concave down on the interval from negative infinity to zero. And so what I've drawn already is just the vertical ascent to X is equal to zero. And I put on the X axis this point negative too. Since that's the point where we go from increasing to decreasing. So I'm just gonna put a point up here as the point that we go from increasing to decreasing, which means that it is a local maximum. Or it could be an absolute maximum as well, but we're guaranteed to have a maximum at this point since we're going from increasing and decreasing. And so I'm going to draw a line that is concave down and increasing up until this point here just call that the point and now we're decreasing. Still concave down and we have this vertical ascent tote so we're never going to go past X is equal to zero. And now what we can do is we can actually just stop there since we don't have any conditions for X being greater than zero. So the important thing to remember is that we're decreasing until X is equal to negative two. And then we are sorry, we're increasing until X is equal to negative two. And then we start decreasing. And since we have this vertical ascent, oh, we're never going to go past zero. And we have to be always concave down which we are Yeah.

View More Answers From This Book

Find Another Textbook

01:31

If a motor pump lifts 2,000 litres of water in 8 minutes, how many will it l…

01:29

Find the square root of 1536 by long division method ?

01:28

Rama planted a total 544 plants in 17 rows. How many plants did she put in e…

01:25

A stationary shop markdown their writing boards by 40%. The markdown is $32.…

02:50

What is the original price of an item that is being charged a tax of 20%, an…

Write a word problem that must be solved with division and includes 2/7 as t…

01:42

In a city, out of every 15 people, 1 person is a government servant. If 1354…

06:56

96 men were engaged for a project of constructing a railway track of the len…

01:41

after purchasing two copies of the same book,x sold the respectively at 0.8 …

03:10

A sum of Rs 30000 invested in a scheme where the interest gets compounded an…