3. Consider the function f (x) = x³. (a) Prove that f is a nondecreasing function by showing f'(x) ≥ 0 for all x. (b) Solve f' (c) = 0 to show that f has a critical number c. (c) Find the intervals for which f is concave up/ concave down.
3. Consider the function f (x) = x³. (a) Prove that f is a nondecreasing function by showing f'(x) ≥ 0 for all x. (b) Solve f' (c) = 0 to show that f has a critical number c. (c) Find the intervals for which f is concave up/ concave down.
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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![3. Consider the function f (x) = x³.
(a) Prove that f is a nondecreasing function by showing f'(x) ≥ 0 for all x.
(b) Solve f' (c) = 0 to show that f has a critical number c.
(c) Find the intervals for which f is concave up /concave down.
(d) Find the location of the inflection point.
(e) Sketch a graph of the function f (x).
(f) Explain why the second derivative test fails in this example.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6484a2ba-7b6c-4144-bd9b-1f2d784a131b%2Ff2b138ed-a430-49d4-8919-46b15e6f18bc%2Fxdmv4e2i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Consider the function f (x) = x³.
(a) Prove that f is a nondecreasing function by showing f'(x) ≥ 0 for all x.
(b) Solve f' (c) = 0 to show that f has a critical number c.
(c) Find the intervals for which f is concave up /concave down.
(d) Find the location of the inflection point.
(e) Sketch a graph of the function f (x).
(f) Explain why the second derivative test fails in this example.
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