Let f(x)=x²+sin x+1 on the interval [1, 2]. Choose the correct statement below. O Since f is not continuous on [1,2], it does not attain its absolute maximum value nor its absolute minimum value. O By the Extreme Value Theorem, f attains both its absolute maximum value and its absolute minimum values. O Since f is not differentiable on [1, 2], it does not attain its absolute maximum value nor its absolute minimum value. O The function f attains only its absolute minimum value. O The function f attains only its absolute maximum value.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Let f(x)=x²+sin x+1 on the interval [1, 2].
Choose the correct statement below.
O Since f is not continuous on [1,2], it does not attain its absolute maximum value nor its absolute minimum value.
O By the Extreme Value Theorem, f attains both its absolute maximum value and its absolute minimum values.
O Since f is not differentiable on [1, 2], it does not attain its absolute maximum value nor its absolute minimum value.
The function f attains only its absolute minimum value.
O The function f attains only its absolute maximum value.
Transcribed Image Text:Let f(x)=x²+sin x+1 on the interval [1, 2]. Choose the correct statement below. O Since f is not continuous on [1,2], it does not attain its absolute maximum value nor its absolute minimum value. O By the Extreme Value Theorem, f attains both its absolute maximum value and its absolute minimum values. O Since f is not differentiable on [1, 2], it does not attain its absolute maximum value nor its absolute minimum value. The function f attains only its absolute minimum value. O The function f attains only its absolute maximum value.
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