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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)5
f'(x) = 5(x+1)4
There 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.
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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.
What else can I help you with?
What is the minimum number of points required to mark all maximum minimum and zeros in a period of a sinusoid?
One period of a sinusoid with no constant component has 1 maximum, 1 minimum,and 1 zero crossing, and 2 zero end-points.Total = 5 points.
Which operation between two polynomials will not always result in a polynomial?
Division of one polynomial by another one.
How do explain how to multiply polynomials?
You simply need to multiply EACH term in one polynomial by EACH term in the other polynomial, and add everything together.
What is the only solid with not even one vertex?
A sphere. All other solids, including cubes, rectangular prisms, and cones all have at least one vertex.
How can you find the generalization for square pentagon and hexagon?
They all have at least one pair of parallel lines
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 maximum?
False
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.
What is the minimum sentence for a felony in California?
At least one year and one day in prison.
What is another way to say at least?
Minority would be one
Are polynomials closed under the operations of subtraction addition and multiplication?
Yes, polynomials are closed under the operations of addition, subtraction, and multiplication. This means that when you add, subtract, or multiply two polynomials, the result is always another polynomial. For example, if ( p(x) ) and ( q(x) ) are polynomials, then ( p(x) + q(x) ), ( p(x) - q(x) ), and ( p(x) \cdot q(x) ) are all polynomials as well. However, polynomials are not closed under division, as dividing one polynomial by another can result in a non-polynomial expression.
What is the minimum number of stars in a star system?
it has to be at least 2 or more stars to be a star system.
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.
Which property of polynomial subtraction says that the difference of two polynomials is always a polynomial?
The property that states the difference of two polynomials is always a polynomial is known as the closure property of polynomials. This property indicates that when you subtract one polynomial from another, the result remains within the set of polynomials. This is because polynomial operations (addition, subtraction, and multiplication) preserve the degree and structure of polynomials. Thus, the difference of any two polynomials will also be a polynomial.
Minimum number of directors in private company?
Minimum number of director in a private company is 2.
Minimum age for office of Representives?
The minimum age one must be for the House of Representatives is 25 years old. One must also be a US citizen for at least 7 years.
Is being unpaid for working illegal?
Absolutely, it is illegal. All workers must be paid at least the minimum wage, as specified by federal or state law (whichever one is higher).
