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onsider the function f(x) = = x* + 2x. a) Find the x- and y-intercepts of the ronh of € Gf onu)

onsider the function f(x) = = x* + 2x. a) Find the x- and y-intercepts of the ronh of € Gf onu)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Work Problem 1 ( Consider the function f(x) = x* + 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 function f such that: f' > 0 and f" < 0, for x < 3 f' > 0 and f" > 0, for x > 3. (b) Does the graph of the function f in Part (a) have an inflection point? Explain.
Transcribed Image Text:Work Problem 1 ( Consider the function f(x) = x* + 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 function f such that: f' > 0 and f" < 0, for x < 3 f' > 0 and f" > 0, for x > 3. (b) Does the graph of the function f in Part (a) have an inflection point? Explain.
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