Exploring Inflection Points of x(ln(x))

  • Thread starter Greywolfe1982
  • Start date
  • Tags
    Points
In summary, the conversation discusses the question of finding inflection points for the function f(x)=xlnx and the discrepancies found on WolframAlpha. The individual asking the question is informed that the function has no inflection points and is concave up within its domain, but WolframAlpha shows a real part for x<=0. It is then clarified that the function has complex numbers, resulting in both real and imaginary parts when x<0.
  • #1
Greywolfe1982
62
0
Finding inflection points of x(ln(x)) (or "Why is WolframAlpha telling me this?")

The question is finding the points of inflection for f(x)=xlnx. As far as I know, it has none, and is concave up for the entire function within its domain, x>0. When I look at the graph on WolframAlpha though, it's telling me there's a real part to the function for x<=0. Would somebody care to explain what I'm missing? Or is it a glitch on WolframAlpha's part?

Here's the output:
http://www.wolframalpha.com/input/?i=x(lnx)
 
Physics news on Phys.org
  • #4


It's a complex number. Therefore it has real and imaginary parts when [tex]x<0[/tex].
 

1. What is an inflection point?

An inflection point is a point on a curve where the curve changes from being concave up to concave down, or vice versa. In other words, it is where the curvature of the curve changes direction.

2. How do you find the inflection points of x(ln(x))?

To find the inflection points of x(ln(x)), you need to take the second derivative of the function and set it equal to zero. Then, solve for x. The resulting values of x are the inflection points.

3. What is the significance of inflection points in x(ln(x))?

Inflection points in x(ln(x)) can indicate where the rate of change of the function is changing. This can be helpful in understanding the behavior of the function and predicting future values.

4. Can there be more than one inflection point in x(ln(x))?

Yes, there can be multiple inflection points in x(ln(x)). This is because the function x(ln(x)) can have multiple points where the curvature changes direction.

5. How can I use inflection points in x(ln(x)) in real-world applications?

Inflection points in x(ln(x)) can be useful in various fields such as economics, biology, and physics. For example, in economics, inflection points can help identify the optimal point of production for a certain product. In biology, inflection points can indicate the optimal conditions for growth of a population. In physics, inflection points can help determine the stability of a system.

Similar threads

Inflection Point Calculation: Reduction of Cubic with Second Derivative Method
    • Calculus and Beyond Homework Help
Replies
1
Views
478
Exploring the Sign of a 2nd Derivative Function
    • Calculus and Beyond Homework Help
Replies
7
Views
1K
Where are the extrema and inflection points for the function y = x/ln(x)?
    • Calculus and Beyond Homework Help
Replies
11
Views
1K
Graphing Derivatives: Concavity and Inflection Points
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
MHB Find where increasing/decreasing, concavity, local extrema and inflection points for f(x)=ln/x
    • Calculus
Replies
1
Views
1K
Determine the values of a and b that have inflection points
    • Calculus and Beyond Homework Help
Replies
18
Views
1K
Finding the Inflection points of x^2-4√x
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
Queries regarding Inflection Points in Curve Sketching
    • Calculus and Beyond Homework Help
Replies
2
Views
2K
Inflection Point Without Sign Change
    • Calculus and Beyond Homework Help
Replies
9
Views
2K
B Second derivatives and inflection points
    • Calculus
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top