371. Which of the two functions

$$
y=1000 x \text { and } y=\frac{x^{2}}{1000}
$$

increases faster as $x$ increases from 0 to $+\infty$?
371. The increment of $y=1000 x$ will be $1000(x+h)-1000 h=$ $=1000 h$;

the increment of $y=\frac{x^{2}}{1000}$ will be $\frac{(x+h)^{2}}{1000}-\frac{x^{2}}{1000}=\frac{2 x h+h^{2}}{1000}$, or approximately $\frac{2 x h}{1000}$.

Let: $\frac{2 x h}{1000}1000 h$, from which $x>500$ 000. Therefore: for $0<x<5000001000 x$ increases faster than $\frac{x^{2}}{1000}$; starting from $x=500000$ the function $\frac{x^{2}}{1000}$ increases faster than $1000 x$.