Sketch the graph of a function f which incorporates all the limit & derivative information below: (Be sure to include any asymptotes in your sketch of the graph f) • lim f(x)=0 lim f(x)=−∞ lim f(x)=∞ limf(x)=−∞ lim f(x)=1 • The function values of f, and its first derivative f′(x), and its second derivative, f′′(x), are undefined at x = −2 and at x = 0, and are defined for all other real number values of x. • The first derivative f′(x) is negative on the x-intervals (−∞, −2) and (−2, 0), is positive on the interval (0, 2), is zero at x = 2, and is negative on the interval (2, ∞). • The second derivative f′′(x) is negative on the x-interval (−∞,−2), positive on the interval (−2, −1), has value zero at x = −1, is negative on the intervals (−1, 0) and (0, 3), has value zero at x = 3, and is positive on the interval (3, ∞). 10. Sketch the graph of a function f which incorporates all the limit & derivative informationbelow:(Be sure to include any asymptotes in your sketch of the graph f)lim f(x) = 0lim f(x)lim f(x) = 00lim f(x) = -∞ lim f(x) = 1= -00x -00I-2-r-2+• The function values of f, and its first derivative f'(x), and its second derivative, f"(x),are undefined at x = -2 and at x = 0, and are defined for all other real number valuesof x.• The first derivative f'(x) is negative on the x-intervals (-o, -2) and (-2, 0), is positiveon the interval (0, 2), is zero at x = 2, and is negative on the interval (2, 00).• The second derivative f"(x) is negative on the x-interval (-∞, -2), positive on theinterval (-2, –-1), has value zero at z = -1, is negative on the intervals (-1,0) and(0, 3), has value zero at x = 3, and is positive on the interval (3, o0).

We have to graph the given function.

Answered: 10. Sketch the graph of a function f…

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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Sketch the graph of a function f which incorporates all the limit & derivative information below: (Be sure to include any asymptotes in your sketch of the graph f) • lim f(x)=0 lim f(x)=−∞ lim f(x)=∞ limf(x)=−∞ lim f(x)=1 • The function values of f, and its first derivative f′(x), and its second derivative, f′′(x), are undefined at x = −2 and at x = 0, and are defined for all other real number values of x. • The first derivative f′(x) is negative on the x-intervals (−∞, −2) and (−2, 0), is positive on the interval (0, 2), is zero at x = 2, and is negative on the interval (2, ∞). • The second derivative f′′(x) is negative on the x-interval (−∞,−2), positive on the interval (−2, −1), has value zero at x = −1, is negative on the intervals (−1, 0) and (0, 3), has value zero at x = 3, and is positive on the interval (3, ∞).

10. Sketch the graph of a function f which incorporates all the limit & derivative information
below:
(Be sure to include any asymptotes in your sketch of the graph f)
lim f(x) = 0
lim f(x)
lim f(x) = 00
lim f(x) = -∞ lim f(x) = 1
= -00
x -00
I-2-
r-2+
• The function values of f, and its first derivative f'(x), and its second derivative, f"(x),
are undefined at x = -2 and at x = 0, and are defined for all other real number values
of x.
• The first derivative f'(x) is negative on the x-intervals (-o, -2) and (-2, 0), is positive
on the interval (0, 2), is zero at x = 2, and is negative on the interval (2, 00).
• The second derivative f"(x) is negative on the x-interval (-∞, -2), positive on the
interval (-2, –-1), has value zero at z = -1, is negative on the intervals (-1,0) and
(0, 3), has value zero at x = 3, and is positive on the interval (3, o0).

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