Graphing a Rational Function Using First and Second Derivatives

In this video, we will graph a rational function by finding intercepts, asymptotes, critical values, and inflection points. We use First and Second derivative sign charts to analyze intervals of increasing or decreasing values and to analyze concavity (up or down).

[odalfrypolonia]

odalfry polonia, MAC2233, always struggled with sign charts. after analyzing this video I got the grasp of it. thanks professor.

[nicolemartinez]

Nicole Martinez, MAC2233, I learned a lot from watching this video, but the main thing was how important the step by step processes is to properly graph the functions. It helped me understand how to do it properly and efficiently so that mistakes would not be made, especially on the test where it matters. I learned how to use the first derivative and second derivative to find the answers! Thank you!!

[dewaynefullwood]

Jeremy Fullwood, MAC2233, One takeaway was when to utilize the first and second derivatives to find the intercepts, asymptotes, where the function is increasing and decreasing, etc. Thank you for the video Professor Hearn, it was really helpful.

[rachel.mayahh]

Rachel Fertil MAC2233
One takeaway from this video is how I need to take it step by step to graph these functions properly. I learned how to use the first and second derivatives to properly graph functions, and it cleared up a lot of questions I had from previous years. Thank you, Professor Hearn!

[williamgarzon]

Will G.
MAC2233
One thing I liked about the video was to know how important it is to find the asymptotes, thank you Ms. Hearn!

[nataliabain]

Natalia Bain, MAC2233, Your videos have continued to help me go over certain concepts that have not stuck yet. You give a clear step by step in depth way of being able to solve the problem.
Thank you!!

[jonathanturjeman]

Jonathan Turjeman, MAC2233, one thing I liked about the video is how you go in-depth and make it easy to understand

[aaliyah]

Aaliyah Henriquez - MAC2233. One thing I liked about this video is how you take us step by step without leaving room for any confusion. It helped me understand how to graph rational functions and allowed me to understand how to find the second derivative a little better; derivatives are not easy for me at all so this video is a great help.

[giuseppedimauro]

Giuseppe Di Mauro
MAC2311
I learned from this video how to graph both derivatives from a function. This video also helped me to understand the small errors that I would often make. I made a silly error on a test that made me to get the answer wrong. Looking back into this video, I'm now aware of the mistake I made and I will be paying attention for it in the future. Thank you

[juanavillamil]

Juana Villamil
2311
This video reminded me on how to find the asymptotes and also how to find the intercepts. Also, it helped me practice graphic concavity.

[nadermaklad]

Nader Maklad, MAC2233, This video helped me understand how important it is to find the asymptotes and the domain/range of the function. Usually I rush into trying to find all of the critical points and doing the graph that way, but I realized that if I take it step-by-step it would be much easier to find the end product.

[robertogarrido]

Roberto Garrido
MTWR 12:30 MAC2311
2:05 "In a rational function the only place that you're going to have a restricted value, values of x that we are not allowed to plug in is where the denominator is equal to 0."

[GabbyA]

Gabriela Alvarado
MAC2233 @ 11:00AM

The video helped me understand how to analyze each part of the function and take it step by step in order to find all the needed values. I knew how to find intercepts and asymptotes, but this video helped me get a better understanding of finding the second derivatives and how it applies to graphing the rest of the values

[nikihartman]

Allison Hartman
MAC2311 MTWR 12:30
"f double prime is used to find inflection points, which is where it changes concavity. Where is it zero and undefined..."

[maeganstofsky]

Maegan Stofsky
MAC2311 MTWR 12:30
"So we could take that out, the lower of the two. Always take the lower of the two powers."

[sreesreekumar]

Sreelekshmi Sreekumar MTWR 12:30 PM-1:45 PM; f double prime is used to find inflection points and where concavity changes

[chrismalliakis]

Chris Malliakis
MTWR 12:30-1:45
“The points where the graph changes from increasing to decreasing of course are your relative extrema”

[rafisanchez]

Rafhaea Sanchez
MAC2311 MTWR 12:30
"you wanna be aware of your domain and range, so you want to think about that, you want to determine any intercepts, asymptotes, and maybe even think about the symmetry of the graph."

[laurynspencer]

Lauryn Spencer
MAC2233
The video helped me understand how to graph my points. I was able to get the points but plotting them correcting in correlation to c.up or c.dn/ increasing and decreasing, always gave me trouble. I also got a better understanding of why it’s important to find where the second derivative is equal to 0 or undefined.

[alicia-pmed]

Hi Professor Hearn! My name is Alicia Dacosta, MAC2233-776. One thing I liked about the video was that you made every very simple and easy to understand, thank you!