Unit 13: Extrema Lecture 13.1. The task to maximize or minimize a function f appears often in applications. As in single variable calculus, the strategy is to look for points, where the …

We can identify two types of extrema - local and global. Global extrema are the largest and smallest values that a function takes on over its entire domain, and local extrema are extrema …

Local and global extrema are much like their counterparts in single variable calculus. They are just points in the domain of a real-valued function where the function value is locally the lowest or …

Second Derivative Test The following theorem is thesecond derivative testfor absolute extrema: Theorem Let c be theonlycritical value of f (x ). (a) If f00(c ) > 0, then f (c ) is a local minimum. …

· A function f (x) has an absolute minimum (or global minimum) at x = b if f(b) ≤f(x) for all x in the domain of the function. f (b) is called the minimum value of f (x). . The maximum and minimum …

(Sometimes we’ll use the word “extrema” to refer to critical points which are either maxima or minima, without specifying which.) For example, consider f(x) = x4 − 2x3. Solving f′(x) = 4x3 − …

3) f(c) is a local extreme value of f if it is either a local maximum or local minimum value. How do we find the local extrema? First Derivative Test Let f be continuous on an open interval (a,b) …