How to Determine Where a Function is Concave Up or Down?

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SUMMARY

The discussion focuses on determining the concavity of the function f(x) = (2x)/((x^2)-25) by analyzing its second derivative. The second derivative was calculated as -4x((-2x^2)-24)/((x^2)-25)^2. The user identified x=0 as the only inflection point but incorrectly concluded the concavity for intervals around this point. The correct analysis reveals that f(x) is concave down for x < 0 and concave up for x > 0, with exceptions at x = -5 and x = 5 needing further verification.

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Homework Statement



f(x)=(2x)/((x^2)-25)

find concave up and down

Homework Equations


The Attempt at a Solution



I found the second derivative to b

-4x((-2x^2)-24)
-----------------
((x^2)-25)^2

i found the only inflection point was x=0 (which was correct)

I plugged in values on both the right and left side of 0 and determined that f(x) was concave down on all values smaller than 0 with the exception of -5, and f(x) was concave up on all values larger than 0 with the exception of 5

however this is not the correct answer. Can someone confirm/tell me what i am doing wrong?

thanks
 
Last edited:
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Something is wrong with your calculations as that is not correct for the second derivative.
 

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