MATH0801 Lecture 3: p) Chapter 4 Filled-3
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Similarly, we say f x has a local minimum value on d at a point f x f c for all x in some open interval containing c. c if. If the inequalities in the above definition are true for all x in the domain of f, we say f c is an absolute maximum/minimum value. Definition: a critical number of a function f is a value x within its domain where f " x =0 or f " x doesn"t exist. Local (and hence absolute) extrema can only occur at critical numbers or endpoints of the domain. If f is continuous on closed and bounded interval [ a , b] , then f surely attains both an absolute max and an absolute min on [ a , b] . Find the absolute max/min of f (t)= 3 t (8 t) on the interval [ 0,8] .
