Can a polynomial with an odd degree have absolute maxima or minima?

An odd polynomial of degree higher than three will look much like a cubic, and may contain more than one curve. Since odd functions have opposite end behavior, there is never an absolute maximum or minimum.

Can both even and odd degree polynomial functions have local maximums and minimums and absolute maximums and minimums?

An odd-degree polynomial can have only local maximums and minimums because the y-value goes to -∞ and ∞ at each end of the function. An even-degree polynomial can have an absolute maximums and minimums because it will go to either -∞ at both ends or ∞ at both ends of the function.

Can an odd function have an absolute minimum?

For odd degree polynomial functions, absolute maximum or absolute minimum values do not exist. Because the end behaviors are opposite, one end approaches to positive infinity (+and the other end approaches to negative infinity (- ).

Can odd degree polynomial graphs have absolute extrema?

Other functions, such as odd-degree polynomials or logarithmic functions, do not have absolute extrema, as their ranges are (-с, с).

Can an odd degree polynomial be an even function?

If f(x) is an even degree polynomial with negative leading coefficient, then f(x) → -∞ as x →±∞. If f(x) is an odd degree polynomial with positive leading coefficient, then f(x) →-∞ as x →-∞ and f(x) →∞ as x → ∞….Polynomial Functions.

Can a polynomial function have an absolute max and min?

Explanation: First of all, by polynomial rules, there will be no absolute maximum or minimum. This is a polynomial function defined over all values of x . Our only critical point will come when the derivative equals 0 .

Why do even degree polynomials have a restricted range?

The range of a polynomial function of even degree is bounded either from below or above because the function will always have a maximum or minimum value.

Which polynomial does not have an absolute maximum?

For example, the linear function f ( x ) = x f(x)=x f(x)=xf, left parenthesis, x, right parenthesis, equals, x doesn’t have an absolute minimum or maximum (it can be as low or as high as we want).

Do polynomials have absolute maximums or minimums?

Explanation: First of all, by polynomial rules, there will be no absolute maximum or minimum.

Are all odd functions odd degree polynomial functions?

A polynomial is even if each term is an even function. A polynomial is odd if each term is an odd function. A polynomial is neither even nor odd if it is made up of both even and odd functions.

Can a polynomial have local extrema without having any real zeros?

Simple answer: it’s always either zero or two. In general, any polynomial function of degree n has at most n−1 local extrema, and polynomials of even degree always have at least one. In this way, it is possible for a cubic function to have either two or zero.