homework help > math > calculus q&a board > topic: plot any stationary points and any points of inflecti...

Q BgQuestion:

      
Pupil
Karma Points: 50
Respect (82%):
posted by  Charmica on 11/3/2009 11:34:28 PM  |  status: Live  |  Earned Karma: 50

Plot any stationary points and any points of inflection. Show any horizontal and vertical asymptotes.

Course Textbook Chapter Problem Needs by
Calculus Calculus and Its Applications (9th) by Bittinger, Ellenbogen N/A N/A 11/4/2009 at 10:00:00 AM
Question Details:
Plot any stationary points and any points of inflection.  Show any horizontal and vertical asymptotes.
   
The denominator should be raised to the 2nd power.  (x+1)^2
Bonus Point Alert! Earn +8 additional karma points for helping this platinum member.

AAnswers:

Answer Question Ask for clarification
Oracle
Karma Points: 30,390
(Drexel University)
posted by The Big Unit on 11/4/2009 12:30:52 AM  |  status: Live
Asker's Rating: Helpful   
Response Details:
Here is a helpful picture of the given function:
You will have vertical asymptotes wherever your function is undefined. Your function will be undefined when the denomiator is equal to zero. Setting the denominator equal to zero and solving for x yields:
So you will have a vertical asymptote at
Checking for horizontal asymptotes:
So you will have a horizontal asymptote at
Your stationary points are the values of x in which . Taking the derivative of the given function, setting it equal to zero, and solving for x yields:
So  is your only stationary point.
A point of inflection occurs when the graph of y changes concavity (concave up to concave down or vice versa) or possibly at a point of nondifferentiability. Computing the second derivative yields:
Because  for  and  and  if , this means that y is concave up on  and  and concave down on . This is saying that you have inflection points at
Jon AKA THE BIG UNIT
If you have any questions about the problem, just message me and I will help you out. Hope this helps!
 
"The whole of science is nothing more than a refinement of everyday thinking."
-Albert Einstein (1879-1955)
 
"Accept the challenges so that you can feel the exhilaration of victory."
-General George S. Patton Jr. (1885-1945)
 
"An investment in knowledge always pays the best interest."
-Benjamin Franklin (1706-1790)
 
"Our greatest glory is not in never failing, but in rising up every time we fail."
-Ralph Waldo Emerson (1803-1882)
 
"Courage is going from failure to failure without losing enthusiasm."
-Winston Churchill (1874-1965)
 
"Unrest of spirit is a mark of life;one problem after another presents itself and in the solving of them we can find our greatest pleasure."
-Karl Augustus Menninger (1893-1990)
 
"That government is best which governs least."
-Thomas Paine (1737-1809)
 
"The pacifist is as surely a traitor to his country and to humanity as is the most brutal wrongdoer."
-Former U.S. President Theodore D. Roosevelt (1858-1919)
 
"A man's country is not a certain area of land, of mountains, rivers, and woods, but it is a principle; and patriotism is loyalty to that principle."
-George William Curtis (1824-1892)
***11/19/09 MIAMI 24 CAROLINA 17 5-5 OVERALL***
 
***11/21/09 MICHIGAN 0 OHIO STATE 0 5-6 OVERALL***
Answer Question Ask for clarificarion
Ask New Question

Join Cramster's Community

Cramster.com brings together students, educators and subject enthusiasts in an online study community. With around-the-clock expert help and a community of over 100,000 knowledgeable members, you can find the help you need, whenever you need it. Join for free today » How Cramster is different from tutoring »

Need Help In

Useful Links