Consider the graph of a function f. Identify the correct statements about the graph. O f'(x) > 0 for all x f has one local minimum and one local maximum. f"(x) < 0 for x > 0 f has one inflection point. f' (x) < 0 for all x O f"(x) > 0 for x < 0

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 graph of a function f.
y
Identify the correct statements about the graph.
f'(x) > 0 for all x
f has one local minimum and one local maximum.
f"(x) < 0 for x > 0
f has one inflection point.
f'(x) < 0 for all x
f"(x) > 0 for x < 0
Transcribed Image Text:Consider the graph of a function f. y Identify the correct statements about the graph. f'(x) > 0 for all x f has one local minimum and one local maximum. f"(x) < 0 for x > 0 f has one inflection point. f'(x) < 0 for all x f"(x) > 0 for x < 0
Determine the intervals on which the function is concave up or down and find the points of inflection.
f(x) = 6x³ – 11x² + 7
(Give your answer as a comma-separated list of points in the form (* , *). Express numbers in exact form. Use symbolic
notation and fractions where needed.)
points of inflection:
Determine the interval on which f is concave up.
(Give your answer as an interval in the form (*, *). Use the symbol co for infinity, U for combining intervals, and an
appropriate type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter Ø if the interval is
empty. Express numbers in exact form. Use symbolic notation and fractions where needed.)
Determine the interval on which f is concave down.
(Give your answer as an interval in the form (*, *). Use the symbol co for infinity, U for combining intervals, and an
appropriate type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter Ø if the interval is
empty. Express numbers in exact form. Use symbolic notation and fractions where needed.)
Transcribed Image Text:Determine the intervals on which the function is concave up or down and find the points of inflection. f(x) = 6x³ – 11x² + 7 (Give your answer as a comma-separated list of points in the form (* , *). Express numbers in exact form. Use symbolic notation and fractions where needed.) points of inflection: Determine the interval on which f is concave up. (Give your answer as an interval in the form (*, *). Use the symbol co for infinity, U for combining intervals, and an appropriate type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter Ø if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) Determine the interval on which f is concave down. (Give your answer as an interval in the form (*, *). Use the symbol co for infinity, U for combining intervals, and an appropriate type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter Ø if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.)
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