# Can a point of inflection be undefined?

See the explanation section below.

Don't use plagiarized sources. Get Your Custom Essay on
Can a point of inflection be undefined?
Just from \$13/Page

A point of inflection is a point on the graph at which the concavity of the graph changes.

If a function is undefined at some value of ##x##, there can be no inflection point.

However, concavity can change as we pass, left to right across an ##x## values for which the function is undefined.

Example

##f(x) = 1/x## is concave down for ##x < 0## and concave up for ##x > 0##.

The concavity changes “at” ##x=0##.

But, since ##f(0)## is undefined, there is no inflection point for the graph of this function.

graph{1/x [-10.6, 11.9, -5.985, 5.265]}

Example 2

##f(x) = root3x## is concave up for ##x < 0## and concave down for ##x > 0##.

##f'(x) =1/(3root3x^2)## and ##f'(x) =(-2)/(9root3x^5)##

The second derivative is undefined at ##x=0##.

But, since ##f(0)## is defined, there is an inflection point for the graph of this function. Namely, ##(0,0)##

graph{x^(1/3) [-3.735, 5.034, -2.55, 1.835]}

## Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
\$26
The price is based on these factors:
Number of pages
Urgency
Basic features
• Free title page and bibliography
• Unlimited revisions
• Plagiarism-free guarantee
• Money-back guarantee
On-demand options
• Writer’s samples
• Part-by-part delivery
• Overnight delivery
• Copies of used sources
Paper format
• 275 words per page
• 12 pt Arial/Times New Roman
• Double line spacing
• Any citation style (APA, MLA, Chicago/Turabian, Harvard)

# Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

### Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

### Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

### Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.