EXAMPLE 8Find the absolute maximum and minimum values of the function below.f(x) = x3 - 3x2 + 215SOLUTION Since f is continuous onwe can use the Closed Interval Method:10f(x) = x3 - 3x² + 2f'(x) =5that is, x = o or x =346Since f'(x) exists for all x, the only critical numbers off occur when f'(x) =Notice that each of these criticalnumbers lies in(- 4). The values of f at these critical numbers aref(0) =andf(2) =The values of f at the endpoints of the interval are(-) -Cand 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 fis sketchedin the figure.

Answered: Image /qna-images/answer/080da88e-8e84-4097-895f-3dea4d5b0093.jpg

EXAMPLE 8 Find the absolute maximum and minimum values of the function below. F(x) = x³ - 3x² + 2 (- 4), we can use the Closed Interval Method: SOLUTION Since fis continuous on f(x) = x³ - 3x2 + 2 F'(x) = |, that is, x = 0 or x =| Since f'(x) exists for all x, the only critical numbers of f occur when f'(x) = [ numbers lies in (- 4). The values of f at these critical numbers are Notice that each of these critical (0) = | and f(2) = | The values of f at the endpoints of the interval are and f(4) = Comparing these four numbere we see that the ahsolute mavimum value is ff4) and the ahsolute minimum value is f2)

EXAMPLE 8 Find the absolute maximum and minimum values of the function below. F(x) = x³ - 3x² + 2 (- 4), we can use the Closed Interval Method: SOLUTION Since fis continuous on f(x) = x³ - 3x2 + 2 F'(x) = |, that is, x = 0 or x =| Since f'(x) exists for all x, the only critical numbers of f occur when f'(x) = [ numbers lies in (- 4). The values of f at these critical numbers are Notice that each of these critical (0) = | and f(2) = | The values of f at the endpoints of the interval are and f(4) = Comparing these four numbere we see that the ahsolute mavimum value is ff4) and the ahsolute minimum value is f2)

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

Chapter5: A Survey Of Other Common Functions

Section5.4: Combining And Decomposing Functions

Problem 14E: Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and...

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