# How many local maximums can a function have?

## How many local maximums can a function have?

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.

## Can a function have multiple maximums?

Important: Although a function can have only one absolute minimum value and only one absolute maximum value (in a specified closed interval), it can have more than one location (x values) or points (ordered pairs) where these values occur.

**Can local minimum be greater than local maximum?**

This example shows that a local minimum may have a value that is greater than a local maximum. In the example, the local maximum value of f is 0, while the local minimum value of f is 4. This is perfectly fine.

### Can a polynomial have two local maxima but no local minima?

No critical point between two peaks If a function of one variable has two local maxima, it must have a local minimum in between.

### Can a cubic polynomial have two local extrema?

A cubic function can also have two local extreme values (1 max and 1 min), as in the case of f(x) = x3 + x2 + x + 1, which has a local maximum at x = −1 and a local minimum at x = 1/3.

**Can a graph have two global maximums?**

Global refers to the entire domain of the function. Global extrema are also called absolute extrema. There can be only one global maximum value and only one global minimum value.

#### What is a local maximum?

The local maximum is a point within an interval at which the function has a maximum value. The absolute maxima is also called the global maxima and is the point across the entire domain of the given function, which gives the maximum value of the function.

#### Can local minimum and local maximum be same?

No it doesn’t ultimately equal 0. It doesn’t have an ultimate value in the same sense that the interval (0, 1] has a maximum value, 1, but not a minimum value (although it does have an infimum, 0).

**Can local maximum value be less than local minimum value?**

Yes, for instance the secant function x↦1cosx has local minima of value 1 at even multiples of π, and local maxima of value −1 at odd multiples of π.

## What is the maximum number of local extrema maxima or minima the graph of the function can have?

1 Expert Answer The number of turning points of a polynomial function of degree n is, at most, n-1. For example, a degree 3 polynomial function has at most 2 local extrema.

## What is local maximum?

A local maximum, also called a relative maximum, is a maximum within some neighborhood that need not be (but may be) a global maximum.

**Does every cubic function have a local maximum and minimum?**

The graph of a cubic function always has a single inflection point. It may have two critical points, a local minimum and a local maximum.