Math Problem Statement
User responses cleared Homework:Section 4.4 Homework Question 8, 4.4.47 Part 4 of 5 HW Score: 91.19%, 10.94 of 12 points Points: 0.14 of 1
Skip to Main content Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10 Question 11 Question 12 Question content area top Part 1 Use the graph of f prime and f double prime to find the critical points and inflection points of f, the intervals on which f is increasing and decreasing, and the intervals of concavity. Then, graph f assuming f(0)equals0. 4 8 12 16 x y font size decreased by 3 y equals f double prime left parenthesis x right parenthesisfont size decreased by 3 y equals f prime left parenthesis x right parenthesis
A coordinate system has a horizontal x-axis labeled from 0 to 16 in increments of 4 and a vertical y-axis. A curve labeled y = f prime (x) starts above the x-axis, falls, crossing the x-axis at 4 to a minimum at x = 8, and rises, crossing the x-axis at 12, to a maximum at 16. A curve labeled y = f double prime (x) starts at the origin, falls to a minimum at x = 4, rises, crossing the x-axis at 8, to a maximum at 12, and falls to the x-axis at 16. Question content area bottom Part 1 Find the critical points. The critical points are xequals 4 comma 12. (Use a comma to separate answers as needed.) Part 2 Find the inflection points. The inflection points occur at xequals 8. (Use a comma to separate answers as needed.) Part 3 Find the intervals on which f is increasing and decreasing. f is increasing on left parenthesis 0 comma 4 right parenthesis comma left parenthesis 12 comma 16 right parenthesis. (Type your answer in interval notation. Use a comma to separate answers as needed.) f is decreasing on left parenthesis 4 comma 12 right parenthesis. (Type your answer in interval notation. Use a comma to separate answers as needed.) Part 4 Find the intervals of concavity. f is concave down on enter your response here. (Type your answer in interval notation. Use a comma to separate answers as needed.) f is concave up on enter your response here. (Type your answer in interval notation. Use a comma to separate answers as needed.) The critical points are x(Use a comma to separate answers as needed.)The inflection points occur at x(Use a comma to separate answers as needed.)f is increasing on(Type your answer in interval notation. Use a comma to separate answers as needed.)decreasingf is decreasing on(Type your answer in interval notation. Use a comma to separate answers as needed.)f is concave down on(Type your answer in interval notation. Use a comma to separate answers as needed.)upf is concave up on(Type your answer in interval notation. Use a comma to separate answers as needed.)Choose the correct graph below.The critical points are x(Use a comma to separate answers as needed.)The inflection points occur at x(Use a comma to separate answers as needed.)f is increasing on(Type your answer in interval notation. Use a comma to separate answers as needed.)decreasingf is decreasing on(Type your answer in interval notation. Use a comma to separate answers as needed.)f is concave down on(Type your answer in interval notation. Use a comma to separate answers as needed.)upf is concave up on(Type your answer in interval notation. Use a comma to separate answers as needed.) Textbook Calculator
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Math Problem Analysis
Mathematical Concepts
Calculus
Critical Points
Inflection Points
Intervals of Increase and Decrease
Concavity
Formulas
f' = 0 at critical points
f'' > 0 indicates concave up
f'' < 0 indicates concave down
Theorems
First Derivative Test
Second Derivative Test
Suitable Grade Level
Grades 11-12
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