3) Curve Sketching: The function y = f(x) and its derivatives are given below. Use the information to complete the tables and to determine a) any asymptotes b) intervals where f(x) is increasing or decreasing c) coordinates of any local minimums or maximums d) intervals where the graph is concave up or down d) coordinates of any inflection points and e) to use the information to sketch the graph of the function. Indicate all features on your graph. (A plot given by graphing software with no other information will receive no credit.) First Derivative Interval Second Derivative Interval f(x)= = 1+x V√√x -; f'(x) = = -1 + 2x = -; f"(x) = 3x√x Sign of f'(x) Sign of f'(x) sketch the graph according to the information above: Determine the following (if any): Local maximums/minimums asymptotes (Show any limits involved) 4 - 2x 9x²√x f(x) Increasing/Decreasing f(x) Concavity ; inflection points
3) Curve Sketching: The function y = f(x) and its derivatives are given below. Use the information to complete the tables and to determine a) any asymptotes b) intervals where f(x) is increasing or decreasing c) coordinates of any local minimums or maximums d) intervals where the graph is concave up or down d) coordinates of any inflection points and e) to use the information to sketch the graph of the function. Indicate all features on your graph. (A plot given by graphing software with no other information will receive no credit.) First Derivative Interval Second Derivative Interval f(x)= = 1+x V√√x -; f'(x) = = -1 + 2x = -; f"(x) = 3x√x Sign of f'(x) Sign of f'(x) sketch the graph according to the information above: Determine the following (if any): Local maximums/minimums asymptotes (Show any limits involved) 4 - 2x 9x²√x f(x) Increasing/Decreasing f(x) Concavity ; inflection points
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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Transcribed Image Text:3) Curve Sketching: The function y = f(x) and its derivatives are given below. Use the information to complete the
tables and to determine a) any asymptotes b) intervals where f(x) is increasing or decreasing c) coordinates of
any local minimums or maximums d) intervals where the graph is concave up or down d) coordinates of any
inflection points and e) to use the information to sketch the graph of the function. Indicate all features on your
graph. (A plot given by graphing software with no other information will receive no credit.)
First Derivative
Interval
Second Derivative
Interval
f(x)=
=
1+x
V√√x
-; f'(x) =
=
-1 + 2x
=
-; f"(x) =
3x√x
Sign of f'(x)
Sign of f'(x)
sketch the graph according to the information above:
Determine the following (if any): Local maximums/minimums
asymptotes (Show any limits involved)
4 - 2x
9x²√x
f(x) Increasing/Decreasing
f(x) Concavity
; inflection points
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