annie1799
Answered

Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Find the absolute maximum of (x^2-1)^3 in the interval [-1,2]

Sagot :

LammettHash

Let f(x) = (x ² - 1)³. Find the critical points of f in the interval [-1, 2]:

f '(x) = 3 (x ² - 1)² (2x) = 6x (x ² - 1)² = 0

6x = 0   or   (x ² - 1)² = 0

x = 0   or   x ² = 1

x = 0   or   x = 1   or   x = -1

Check the value of f at each of these critical points, as well as the endpoints of the given domain:

f (-1) = 0

f (0) = -1

f (1) = 0

f (2) = 27

So max{f(x) | -1 ≤ x ≤ 2} = 27.

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.