# How many turning points can a cubic function have?

Any polynomial of degree ##n## can have a minimum of zero turning points and a maximum of ##n-1##. However, this depends on the kind of turning point.

Don't use plagiarized sources. Get Your Custom Essay on
How many turning points can a cubic function have?
Just from \$13/Page

Sometimes, “turning point” is defined as “local maximum or minimum only”. In this case:

• Polynomials of odd degree have an even number of turning points, with a minimum of 0 and a maximum of ##n-1##.
• Polynomials of even degree have an odd number of turning points, with a minimum of 1 and a maximum of ##n-1##.

However, sometimes “turning point” can have its definition expanded to include “stationary points of inflexion”. For an example of a stationary point of inflexion, look at the graph of ##y = x^3## – you’ll note that at ##x = 0## the graph changes from convex to concave, and the derivative at ##x = 0## is also 0.

If we go by the second definition, we need to change our rules slightly and say that:

• Polynomials of degree 1 have no turning points.
• Polynomials of odd degree (except for ##n = 1##) have a minimum of 1 turning point and a maximum of ##n-1##.
• Polynomials of even degree have a minimum of 1 turning point and a maximum of ##n-1##.

So, in part, it depends on the definition of “turning point”, but in general most people will go by the first definition.

## 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.