EXAMPLE 8 Find the absolute maximum and minimum values of the function below. f(x) = x³ - 3x² + 2 15 SOLUTION Since fis continuous on we can use the Closed Interval Method: 10아 f(x) = x³ - 3x² + 2 f'(x) = 3 4 Since f'(x) exists for all x, the only critical numbers of f occur when f'(x) =| 5 6 that is, x = 0 or Notice that each of these critical numbers lies in The values of f at these critical numbers are f(0) = and f(2) = The values of f at the endpoints of the interval are and f(4) = | Comparing these four numbers, we see that the absolute maximum value is f(4) = and the absolute minimum value is f(2) = Note that in this example the absolute maximum occurs at an endpoint, whereas the absolute minimum occurs at a critical number. The graph of f is sketched in the figure.

EXAMPLE 8 Find the absolute maximum and minimum values of the function below. f(x) = x³ - 3x² + 2 15 SOLUTION Since fis continuous on we can use the Closed Interval Method: 10아 f(x) = x³ - 3x² + 2 f'(x) = 3 4 Since f'(x) exists for all x, the only critical numbers of f occur when f'(x) =| 5 6 that is, x = 0 or Notice that each of these critical numbers lies in The values of f at these critical numbers are f(0) = and f(2) = The values of f at the endpoints of the interval are and f(4) = | Comparing these four numbers, we see that the absolute maximum value is f(4) = and the absolute minimum value is f(2) = Note that in this example the absolute maximum occurs at an endpoint, whereas the absolute minimum occurs at a critical number. The graph of f is sketched in the figure.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter1: Functions

Section1.2: Functions Given By Tables

Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...

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