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Determining concavity of f(x) = x^2 + 2x/(x-2)^2

  • Thread starter Bob Ho
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  • #1
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Hi, sorry to disturb you,
But with the equation f(x)= x^2+2x/(x-2)^2

I need to find the intervals at which f(x) is concave up, and down.

I found f '(x)= (2x+2)(x-2)^2 -2(x-2)(x^2+x)/((x-2)^4)

From there I equated it to 0, and found the critical points to be x=2,-2/3.

However, I have just noticed there is a point of inflection at x=-2. How did I miss this point in my calculation for critical points, any help would be much obliged.

Thanks
 
Last edited:

Answers and Replies

  • #2
Dick
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A point of inflection is not necessarily a critical point. To know about concavity and points of inflection you need to compute the second derivative.
 
  • #3
Defennder
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To find points of inflection, find the values of x for which f''(x) is zero.
 
Last edited:
  • #4
HallsofIvy
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More specifically, where the second derivative changes sign. A point where the second derivative is 0 may not be a point of inflection.
 

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