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Dalia S.

asked • 06/19/14

Find the open intervals on which f is concave up (down). Then determine the x-coordinates of all inflection points of f.

Let f(x)=(7x-2)/(x+2). Find the open intervals on which f is concave up (down). Then determine the x-coordinates of all inflection points of f. 
1. f is concave up on which intervals?
2. f is concave down on which intervals?
3. the inflection points occur at x =?
 
Please provide final answers. 

1 Expert Answer

By:

James F. answered • 06/20/14

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5 (6)

Statistics Graduate Student and Tutor

Jessica S.

what would be the final answers?
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06/20/14

James F.

What do you think the answers are?  I'd be happy to validate them.
 
J.T.
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06/20/14

Jessica S.

if i plug in lets say -3 and -1 in the second deritative function, i get solutions such as -32 however how would i denote that in interval notation?
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06/20/14

James F.

So the second derivative is -32/(x+2)^3    <---I had a typo above before
We plug in x = -3 and get 32
We plug in x = -1 and get -32
 
Since x = -2 is a critical value, we'll use it as the end point of our intervals.
 
f(x) is concave up on (-∞,-2) and concave down on (-2,∞).  Now you can double check you intervals: if you pick ANY number less than -2, f''(x) will always be positive.  If you pick any number greater than -2, f''(x) will always be negative.
 
J.T.
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06/21/14

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