Work Problem 1 ( Consider the function f(x) = x4 + 2x3. (a) Find the x- and y-intercepts of the graph of f (if any). (b) Find the intervals on which f is increasing or decreasing and the local extreme values (x- and y-coordinates) of f. (c) Find the intervals of concavity and inflection points of f. (d) Sketch the graph of f. Work Problem 2 (
Work Problem 1 ( Consider the function f(x) = x4 + 2x3. (a) Find the x- and y-intercepts of the graph of f (if any). (b) Find the intervals on which f is increasing or decreasing and the local extreme values (x- and y-coordinates) of f. (c) Find the intervals of concavity and inflection points of f. (d) Sketch the graph of f. Work Problem 2 (
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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![Work Problem 1 (
Consider the function f(x) = x4 + 2x.
(a) Find the x- and y-intercepts of the graph of f
(if any).
(b) Find the intervals on which f is increasing or
decreasing and the local extreme values (x- and
y-coordinates) of f.
(c) Find the intervals of concavity and inflection
points of f.
(d) Sketch the graph of f.
Work Problem 2 (
(a) Sketch a graph of a functionf such that:
fl > 0 and f" < 0, for a < 3
f' > 0 and f"> 0, for a > 3.
(b) Does the graph of the function f in Part (a)
have an inflection point? Explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e9e0074-cec3-43bd-97c4-516989d57ace%2F1ac1e419-2a97-4b06-85ea-172711d39161%2F4w5lnqk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Work Problem 1 (
Consider the function f(x) = x4 + 2x.
(a) Find the x- and y-intercepts of the graph of f
(if any).
(b) Find the intervals on which f is increasing or
decreasing and the local extreme values (x- and
y-coordinates) of f.
(c) Find the intervals of concavity and inflection
points of f.
(d) Sketch the graph of f.
Work Problem 2 (
(a) Sketch a graph of a functionf such that:
fl > 0 and f" < 0, for a < 3
f' > 0 and f"> 0, for a > 3.
(b) Does the graph of the function f in Part (a)
have an inflection point? Explain.
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