Global Minima

Q.

N characters of information are held on magnetic tape, in batches of x character each; the batch processing time is $\alpha +\beta x^2$ seconds, $\alpha ,\beta$ are constants. The optimum value of x for fast processing is

1. $\frac{\alpha }{\beta }$

2. $\frac{\beta }{\alpha }$

3. $\sqrt{\frac{\alpha }{\beta }}$

4. $\sqrt{\frac{\beta }{\alpha }}$