what is difference between local and absolute values of function?

Question

i m reffering to application of derivatives,calcalus,maths

Answer 1

We are usually talking about points on the function which are maximum or minimum values of f(x). If a function shoots upward from - infinity and crosses the x-axis, reaches a maximum value of f(x) = 2, turs around and shoots downward to a minimum of f(x) = -5, then turns around again and shoots upward toward + infinity, then it has one local maximum of 2 and one local minimum of -5.

The absolute max and min (also called the global max and min) are the smallest and largest values of f(x) over the entire domain. So in the example absolute min = - infinity and absolute max =
+ infinity.

Answer 2

Absolute Maximum Value

Answer 3

You generally talk about local versus absolute in reference to maxima and minima of a function. For example, a local maximum is a point on a (continuous) graph that is higher than the points immediately around it. An absolute, or global, maximum is the maximum value of the graph of all x-values in question.
For example:
y = -x^2 has a local and global maximum at (0,0) as long as x=0 is a member of the domain.
For y = x(x+1)(x-1) = x^3 - x, there is a local maximum at x = -3^(-1/2) or about -.577. If the domain is all x values, then the global or absolute maximum of the function is infinity because limit as x approaches infinity of x^3-x is infinity.

Local maxima and minima can always be found for differentiable functions by setting the first derivative equal to zero.

Answer 4

What I remember about local and absolute special values of a function are maximum and minimum values.

It is said that the max or min is local if it is defined in a specified finite interval within the domain.

It is said that the max o min is absolute if it is defined into the complete domain of the function.

Good luck!