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# Do all polynomials have at least one maximum?

Updated: 4/28/2022

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14y ago

False

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14y ago

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Q: Do all polynomials have at least one maximum?
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### All polynomials have at least one maximum?

Not quite. The point at infinity cannot be regarded as a maximum since the value will continue to increase asymptotically. As a result no polynomial of odd degree can have a maximum. Only polynomials of an even degree whose leading coefficient is negative will have a global maximum.

### All polynomials have at least one minimum?

No. For example all polynomials of the form y=xn (or sums of such positive terms) where n is a positive odd number do not have a minimum.

### Do all polynomials have at least one minimum?

Polynomials of an even degree will always have either a minimum point, or a maximum point, or both.Polynomials of an odd degree may or may not have minima or maxima. If, for example, a polynomial function is simply a transformation of xn, there will be no turning points. For example:f(x) = x5 + 5x4 + 10x3 + 10x2 + 5x + 1 = (x+1)5f'(x) = 5(x+1)4There is only one solution for f'(x) = 0, which is of course x = -1. Since the range of f(x) includes all the real numbers, it follows that this solution represents a point of inflection, and not a turning point.If a polynomial of odd degree does have any turning points, it will have at least one minimum point. It cannot have maximum points only.* * * * *Polynomials of an odd degree cannot have a global maximum or minimum because if the leading coefficient is positive, it goes asymptotically from minus infinity to plus infinity and the other way around if the leading coefficient is negative.

### Are all polynomials either even or odd?

No. Polynomials are made up of several terms. The terms can be even or odd (assuming they aren't variables, in which case, you don't know if they're even or odd), but the polynomial itself isn't one or the other.

### What is the maximum number of Friday the 13th in one calendar year?

Three is the maximum and they have to fall in February, March and November as they do in 2009. A normal year will have only one or two. The most is three. The least is one.

### What is a ratio of two polynomials?

It is an algebraic fraction, consisting of (one polynomial) divided by (the other one).

### Do YOU care about how to factor a polynomial?

Do you care weather a random stranger on their computer cares how to factor polynomials. P.S. i do in fact care how to factor polynomials, but i'm most likely in the minority on this one.

### What is maximum pitches should a 12 year old pitch in one game?

i think at least of 65 to 95

### How can you get help with polynomials and other Algebraic problems?

The best way to get help with understanding Algebraic problems on WikiAnswers is to ask a question about a specific type of problem. For example, if you want to know how to multiply polynomials, you could ask "What are the steps needed to multiply polynomials?" There are also some excellent websites that show all the steps to take to solve specific problems. Please see the Related Links below to go to one or more of those websites.

### How many sums of money can be formed from 5 coins if exactly 3 coins are used?

Only one, if all five coins have the same value. Otherwise, 5C3= 10 is the maximum number.Only one, if all five coins have the same value. Otherwise, 5C3= 10 is the maximum number.Only one, if all five coins have the same value. Otherwise, 5C3= 10 is the maximum number.Only one, if all five coins have the same value. Otherwise, 5C3= 10 is the maximum number.

### What is all the number less than 100 that hasat least one 2 and at least one 5 in their prime factorization at least one 2 and at least one 5?

All the even numbers and the odd multiples of 5.

### Do all parallelograms have at least one right angle?

The simple answer is no, not all parallelograms have at least one right angle. However, there are some that do. Rectangles and squares are 'special' parallelograms that all have at least one right angle.