In this post, you will use the first and second derivatives of a function (along with a few other pieces of information) to sketch the graph of a function. Sketch the graph of a single function f (x) that satisfies all of the following conditions. Use the techniques that we have learned in this course to do so. 16(x + 2) (6-x)³ f'(x) = 32(x + 6) (6-x)4 The domain of f is (-∞0, 6) U (6,∞0) x = 6 is a vertical asymptote of f lim f(x) = 1, lim f(x) = 1 *700* f" (x) = f(2)=1 After you have sketched the graph, label the equations of the asymptotes, as well as the locations of any local extrema. Then, explicitly state the intervals of increase and decrease, the intervals of concavity, and the x- coordinates of any inflection points. For your explanation, please describe how the shape of your graph is achieved from the first and second derivatives.
In this post, you will use the first and second derivatives of a function (along with a few other pieces of information) to sketch the graph of a function. Sketch the graph of a single function f (x) that satisfies all of the following conditions. Use the techniques that we have learned in this course to do so. 16(x + 2) (6-x)³ f'(x) = 32(x + 6) (6-x)4 The domain of f is (-∞0, 6) U (6,∞0) x = 6 is a vertical asymptote of f lim f(x) = 1, lim f(x) = 1 *700* f" (x) = f(2)=1 After you have sketched the graph, label the equations of the asymptotes, as well as the locations of any local extrema. Then, explicitly state the intervals of increase and decrease, the intervals of concavity, and the x- coordinates of any inflection points. For your explanation, please describe how the shape of your graph is achieved from the first and second derivatives.
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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Transcribed Image Text:In this post, you will use the first and second derivatives of a function (along with a few other pieces of information) to sketch the graph of a function.
Sketch the graph of a single function f (x) that satisfies all of the following conditions. Use the techniques that we have learned in this course to do so.
16(x + 2)
(6 - x)³
f'(x)
=
32(x + 6)
f" (x)
(6 - x) ¹
The domain of f is (-∞0, 6) U (6,∞)
x = 6 is a vertical asymptote of f
lim f(x) = 1, lim f(x) = 1
30-00
f(2)=1
After you have sketched the graph, label the equations of the asymptotes, as well as the locations of any local extrema. Then, explicitly state the intervals of increase and decrease, the intervals of concavity, and the x-
coordinates of any inflection points.
For your explanation, please describe how the shape of your graph is achieved from the first and second derivatives.
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