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Rookie
Karma Points: 10
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Respect
(100%):
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| Date Posted:
5/25/2008 10:39:45 PM
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Live |
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| Sketch the Graph |
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| Calculus |
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Question Details:
Sketch the graph of f(x) = (x2-x-2)ex. Use the guidelines in the book.
Those guidelines are: domain, x and y intercepts, symmetry, asymptotes, intervals of decrease or increase, local maximum and minimum, critical points, concavity and point of inflections.
Thanks ahead of time for the help.
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| Date Posted:
5/25/2008 10:59:06 PM
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Asker's Rating:
Lifesaver
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Response:
Domain of f(x) is all real #'s
f(x) has no symmetry
Asymptotes:
Horizontal:
as x-->∞ then y-->∞
as x-->-∞ then y-->0
No vertical asymptotes
You must find the first and second derivative...f'(x) and f''(x):
(a) Then, find the critical points ==>where f'(x) = 0 or undef.
The critical points are -2.303 and -5.908
Now make the number line to see where f is increasing or decreasing...
Then,
f is Increasing on: (-∞, -2.303), (1.303, ∞) and f is Decreasing on: (-2.303, 1.303)
Local max: (-2.303, .560)
Local min: (1.303, -5.908)
b.) You need to use the second derivative to find intervals of concavity and inflection points.
Find the critical points: f''(x) = 0 or undef.
Critical points are: -3.562 and .562
Then, intervals of concavity are:
Concave up on: (-∞, -3.562), (.562, ∞)
Concave down on: (-3.562, .562)
Inflection pts. are found where concavity changes...
Thus, the inflections pt. are: (-3.562, .405), (.562, -3.938)
THIS SHOULD BE 100% CORRECT
If you have any questions, ask me.
Please rate
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  Hello - Please Rate if I did your problem
I am only 16 so bare with me if I messed something up!!!
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Oracle
Karma Points: 11,175
(Drexel University)
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| Date Posted:
5/25/2008 11:01:59 PM
Status:
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Response:
Here is a graph of the function  :
Jon AKA THE BIG UNIT
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If you have any questions about the problem, just message me and I will help you out. Hope this helps!
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