Ok so i am a bit confused with this idea.

So you take second derivative and set to zero.

I have this equation

$\displaystyle f''(x) = 24x + \frac{2}{x^{\frac{3}{2}}} = 0 $

So i set to zero and get $\displaystyle x = \sqrt[\frac{5}{2}]{\frac{2}{24}} $

So i take the answer this gives me and plug into f''(x) but i get 17ish. Does this mean i don't have a point on inflextion?

But if it equaled zero then i would?