Whats the difference between abs extreme values and extreme values?

The difference between abs extreme values (absolute extreme values) and extreme values is:
The absolute extreme values, or extrema, refer to the maximum and minimum values of a function while an extreme value, or extremum (plural extrema), is the smallest (minimum) or largest (maximum) value of a function.

>A function f is said to have an absolute maximum on an interval I at x0 if f(x0 ) is the largest value of f on I; that is, f(x0 ) ≥ f(x) for all x in the domain of f that are in I.

What can we do about it

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: the function g(x) has the greatest slope.