Understanding the Turning Point and Asymptote of a Calculus Sketch

  • Thread starter Thread starter aricho
  • Start date Start date
  • Tags Tags
    Calculus Sketch
Click For Summary
SUMMARY

The discussion centers on the function y = x + 4/(x-1), specifically analyzing its turning point, asymptote, and derivatives. The minimum turning point is confirmed at (1/2, 15/4), with an asymptote located at x = 1. Participants express confusion regarding the identification of all lines and the application of limits in calculus, particularly in relation to determining values of y at x = 0 and x at y = 0.

PREREQUISITES
  • Understanding of calculus concepts, specifically derivatives
  • Familiarity with asymptotes and their implications in function behavior
  • Knowledge of evaluating limits in calculus
  • Ability to interpret turning points in graphical analysis
NEXT STEPS
  • Study the concept of limits in calculus to clarify their role in function behavior
  • Learn how to identify and analyze asymptotes in rational functions
  • Explore the process of finding turning points using first and second derivatives
  • Practice evaluating functions at specific points, such as y at x=0 and x at y=0
USEFUL FOR

Students and educators in calculus, particularly those focusing on function analysis, turning points, and asymptotic behavior.

aricho
Messages
71
Reaction score
0
hey guys, having trouble with this one:

y=x + 4/(x-1)

i have found 1st and 2nd derivatives.

Minimum turing point at (1/2, 15/4) and there are no points of inflexion. there is an asympote at x=1...right.

This line is more than just that though isn't it? how can u tell that you got all the lines? we did it in class with limits but i kinda didnt get it.


All help is apprecaited...thanks!
 
Physics news on Phys.org
How about the simple questions like:

What's the value of y at x=0?

and

What's the value of x at y=0?

(You are correct about the asymptote at x=1 - which direction does it go?)

I also get different x-values for the turning point(s).
 
Last edited:

Similar threads

Sketch the graphs of the functions - Calculus question
  • · Replies 3 ·
Replies
3
Views
2K
Area of segment cut from a circle
  • · Replies 2 ·
Replies
2
Views
2K
Sketch the graphs of the functions - Calculus question
  • · Replies 3 ·
Replies
3
Views
2K
Constructing cubic spline interpolation polynomials
  • · Replies 4 ·
Replies
4
Views
2K
Finding x/y-intercepts, asymptotes, derivatives, and max min
  • · Replies 4 ·
Replies
4
Views
2K
Queries regarding Inflection Points in Curve Sketching
  • · Replies 2 ·
Replies
2
Views
2K
Sketch graphs showing vertical & horizontal asymptotes and relative extrema
  • · Replies 2 ·
Replies
2
Views
3K
Possible webpage title: How to Find Asymptotes in a Calculus AB Limits Test?
  • · Replies 4 ·
Replies
4
Views
2K
Finding a Point of Inflexion for f(x)
  • · Replies 3 ·
Replies
3
Views
1K
A few questions to make sure I understand Fourier series
  • · Replies 3 ·
Replies
3
Views
2K