Consider the function f(x) = x³ + x² – x + 6 on the interval [-3, 0]. Find f'(x). f'(x) = 3x + 2x – 1 Find the critical value of f(x) on the interval [-3, 0]. x = -1 Evaluate the function at the critical value. (х, у) %3D -1,5 Evaluate the function at the endpoints of the given interval. (х, у) 3D -3, – 11 (smaller x-value) (х, у) 3 0,4 (larger x-value) Find the absolute maxima and minima for f(x) on the interval [-3, 0]. absolute maximum (х, у) %3D -1,5 absolute minimum (х, у) -3, – 11

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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Consider the function f(x) = x³ + x² – x + 6 on the interval [-3, 0].
Find f'(x).
f'(x) = 3x + 2.x – 1
Find the critical value of f(x) on the interval [-3, 0].
X = -1
Evaluate the function at the critical value.
(х, у) %3D
-1,5
Evaluate the function at the endpoints of the given interval.
(х, у)
-3, – 11
(smaller x-value)
(х, у) %3D
0,4
(larger x-value)
Find the absolute maxima and minima for f(x) on the interval [-3, 0].
absolute maximum
(х, у)
-1,5
absolute minimum
(х, у) 3D
-3, – 11
Transcribed Image Text:Consider the function f(x) = x³ + x² – x + 6 on the interval [-3, 0]. Find f'(x). f'(x) = 3x + 2.x – 1 Find the critical value of f(x) on the interval [-3, 0]. X = -1 Evaluate the function at the critical value. (х, у) %3D -1,5 Evaluate the function at the endpoints of the given interval. (х, у) -3, – 11 (smaller x-value) (х, у) %3D 0,4 (larger x-value) Find the absolute maxima and minima for f(x) on the interval [-3, 0]. absolute maximum (х, у) -1,5 absolute minimum (х, у) 3D -3, – 11
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