Stationary point of inflection

• May 22nd 2013, 04:05 AM
iMagoo
Stationary point of inflection
I have this question that I have been looking at for hours and I'm well and truly over it.

Obviously it's linked to Derivatives and Concavity, but I'm not sure how to go about it.

Attachment 28430

$f(x)=ax^2+bx+c$
$g(x)=f(x)+\frac{\ln(x)}{x^4}=ax^2+bx+c+\frac{\ln(x )}{x^4}$
Now, require $g'(1)=0$ and $g''(1)=0$ and you will get two equations from which you will be able to solve for $a$ and $b$, where $c$ remains a parameter, as it merely shifts the function vertically and so has no bearing on the $x$-coordinate of critical values.