Finding Relative Extrema and Points of Inflection

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• May 13th 2012, 05:02 PM
Bashyboy
Finding Relative Extrema and Points of Inflection
The function is $\displaystyle f(x) = \frac{x^2}{x^2 - 1}$ The answer key claims there to be no points of inflection, yet I found from my second derivative
$\displaystyle f''(x) = \frac{-10x^2 + 2}{(x^2 - 1)^3}$ I find the points $\displaystyle x = \pm\sqrt{\frac{1}{5}}$ Could it be possible that the answer key is wrong?
• May 13th 2012, 05:11 PM
Prove It
Re: Finding Relative Extrema and Points of Inflection
Is it asking for STATIONARY points of inflexion?
• May 13th 2012, 05:13 PM
skeeter
Re: Finding Relative Extrema and Points of Inflection
your second derivative is wrong.

try again ...
• May 13th 2012, 11:35 PM
earboth
Re: Finding Relative Extrema and Points of Inflection
Quote:

Originally Posted by Bashyboy
The function is $\displaystyle f(x) = \frac{x^2}{x^2 - 1}$ The answer key claims there to be no points of inflection, yet I found from my second derivative
$\displaystyle f''(x) = \frac{-10x^2 + 2}{(x^2 - 1)^3}$ I find the points $\displaystyle x = \pm\sqrt{\frac{1}{5}}$ Could it be possible that the answer key is wrong?

Your 2nd derivative is wrong:

$\displaystyle f''(x)=\frac{6x^2+2}{(x^2-1)^3}$

Obviously there isn't a real solution to $\displaystyle f''(x)=0$
• May 14th 2012, 07:16 AM
Bashyboy
Re: Finding Relative Extrema and Points of Inflection
Quote:

Originally Posted by Prove It
Is it asking for STATIONARY points of inflexion?

I never heard of these stationary points of inflection. What is the difference between points of inflection and stationary points of inflection?
• May 14th 2012, 07:22 AM
skeeter
Re: Finding Relative Extrema and Points of Inflection
Quote:

Originally Posted by Bashyboy
I never heard of these stationary points of inflection. What is the difference between points of inflection and stationary points of inflection?

a stationary point of inflection is a point on the curve where f'(x) = 0 , and f''(x) = 0 (and also changes sign)

look at the graph of $\displaystyle y = x^3$ ... it has a stationary point of inflection at x = 0