How to solve this

[Valentas]

I need to find all a values with which g(x) is descending in interval I = (0;5)

\(\displaystyle g(x) = ax^2 - lnx \) I = (0;5)

My job yet: g'(x) < 0 then function descends

\(\displaystyle g'(x) = \frac{2ax^2 -1}{x}\)

Can't solve it...

 

[pka]

I need to find all a values with which g(x) is descending in interval I = (0;5)
\(\displaystyle g(x) = ax^2 - lnx \) I = (0;5)
My job yet: g'(x) < 0 then function descends
\(\displaystyle g'(x) = \frac{2ax^2 -1}{x}\)

You know that \(\displaystyle 0<x<5\).
So every thing depends on the value of \(\displaystyle a\).
Because it must be the case that \(\displaystyle 2ax^2<1\).
What is \(\displaystyle a~?\)

 

[Valentas]

You know that \(\displaystyle 0<x<5\).
So every thing depends on the value of \(\displaystyle a\).
Because it must be the case that \(\displaystyle 2ax^2<1\).
What is \(\displaystyle a~?\)

a < 1/50 ?