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6 and its graph, use the graph to determine the following. r(x) 10 하 6 4 2 -4 -3 -2 -1 -2 1 2 3 4 -8 -10 Find the critical values of (x). (You may assume that all critical values are integers. Enter your answers as a comma-separated list.) Find intervals where f(x) is increasing. (Enter your answer using interval notation.) Find intervals of where (x) is decreasing. (Enter your answer using interval notation.) Find where f(x) has relative maxima, relative minima, and horizontal points of inflection. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) relative maxima relative minima horizontal points of inflection Sketch a possible graph for f(x) that passes through (0, 0). y y y y 15H 15 15 15- 10 1아 10 10 5 5 5 5 -6 -4 -2 2 4 6 -6 -4 -2 2 4 -2 4 6 -6 -4 2 4 -5H -5 -10 -10 -10 -10- -15t -15 -15F -15t

6 and its graph, use the graph to determine the following. r(x) 10 하 6 4 2 -4 -3 -2 -1 -2 1 2 3 4 -8 -10 Find the critical values of (x). (You may assume that all critical values are integers. Enter your answers as a comma-separated list.) Find intervals where f(x) is increasing. (Enter your answer using interval notation.) Find intervals of where (x) is decreasing. (Enter your answer using interval notation.) Find where f(x) has relative maxima, relative minima, and horizontal points of inflection. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) relative maxima relative minima horizontal points of inflection Sketch a possible graph for f(x) that passes through (0, 0). y y y y 15H 15 15 15- 10 1아 10 10 5 5 5 5 -6 -4 -2 2 4 6 -6 -4 -2 2 4 -2 4 6 -6 -4 2 4 -5H -5 -10 -10 -10 -10- -15t -15 -15F -15t

Calculus: Early Transcendentals
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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Given f'(x) = x - x - 6 and its graph, use the graph to determine the following. f"(x) 10 8 6 4 2 X -4 -3 -2 -1 1 2 3. 4 .4 -10 Find the critical values of f(x). (You may assume that all critical values are integers. Enter your answers as a comma-separated list.) X = Find intervals where f(x) is increasing. (Enter your answer using interval notation.) Find intervals of where f(x) is decreasing. (Enter your answer using interval notation.) Find where f(x) has relative maxima, relative minima, and horizontal points of inflection. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) relative maxima relative minima horizontal points of inflection Sketch a possible graph for f(x) that passes through (0, 0). y y y y 15 15 15 15 10 10 10 10 5 5 5 X -6 -4 -2 4 6 6 -4 -2 4 6 -6 - 2 2 4 6 -6 -4 -2 4 6 -5 -5 - 10 -10 - 10 - 10 - 15H -15H -15 -15
Transcribed Image Text:Given f'(x) = x - x - 6 and its graph, use the graph to determine the following. f"(x) 10 8 6 4 2 X -4 -3 -2 -1 1 2 3. 4 .4 -10 Find the critical values of f(x). (You may assume that all critical values are integers. Enter your answers as a comma-separated list.) X = Find intervals where f(x) is increasing. (Enter your answer using interval notation.) Find intervals of where f(x) is decreasing. (Enter your answer using interval notation.) Find where f(x) has relative maxima, relative minima, and horizontal points of inflection. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) relative maxima relative minima horizontal points of inflection Sketch a possible graph for f(x) that passes through (0, 0). y y y y 15 15 15 15 10 10 10 10 5 5 5 X -6 -4 -2 4 6 6 -4 -2 4 6 -6 - 2 2 4 6 -6 -4 -2 4 6 -5 -5 - 10 -10 - 10 - 10 - 15H -15H -15 -15
Expert Solution
Step 1

For critical points. f'(x)=0

The points on the graph that touches the x axis will be the critical points.

The critical points are x=-2,3

The interval in which f'(x) is positive, f(x) will increase, and the interval in which f'(x) is negative f(x) will decrease.

f'(x) is positive in the interval (-∞,-2] ∪[3,∞), hence f(x) is increasing in the interval (-∞,-2] ∪[3,∞)

f'(x) is negative in the interval [-2,3], hence f(x) is decreasing in the interval [-2,3].

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