Here´s the question.

Attachment 19576

Ok so the derivative of f

$\displaystyle {\frac {d}{dx}}f \left( x \right) =\cos \left( x \right) -1+3\,\alpha

\,{x}^{2}

$

The function is monotonically increasing if the derivative of f is bigger than zero in the interval. Or if $\displaystyle \alpha<1/3\,{\frac {1-\cos \left( x \right) }{{x}^{2}}}$

So my task should be to determine the lowest value of the right hand side of the inequality and say that alpha should be less than that? Is it so? I´ve tried that but ended up with zeros in the denominator and stuff. Any ideas?