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Question
I got this question wrong on a test a couple weeks ago, I wanted to revisit this concept in case it's on a future test. I can't get any credit for this question anymore, but I would like to see the correct answer (and hopefully some basic steps), to try and figure out what I did wrong.

Given f(x)=x^4-72x^2-17, identify any inflection points and find the intervals where the function is concave up or down.
Thank you for your assistance, I sincerely appreciate you taking the time to help. Clark

Answer
http://www.wolframalpha.com/input/?i=inflexion+point+x%5E4-72x%5E2-17

To get inflexion point, differentiate your function twice and check when it is zero

becos: first derivative shows whether it's going up or going down (zero => stationary point/max/min)
      second derivative shows whether it's accelerating up or down (zero => inflextion point)

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