can someone tell me what is the difference between a relative max. or min. and an absolute max or min value?
Relative Max: Let be a critical number of a function .
1. If from negative to postive at , then has a relative minimum at
2.If from positive to negative at , then has a relative maximum at
Now let
3. Suppose that is defined over the interval and . Then, if for all , is an absolute maximum for on
A function, f, has an absolute minimum at x= a if f(a) is less than or equal to any value of f(x).
A function, f, has a relative minimum at x= a if f(a) is less than or equal to any value of f(x) on some small interval around a.
For absolute and relative maximum switch "less than" to "larger than".
What VonNemo19 said about relative maximum and minimum is true for differentiable functions.
But the function f(x)= x for all x except 1, f(1)= 2, has a relative maximum at x= 1 even though the derivative, where ever it is defined, never changes sign