175. On the curve $y=x^{2}-3 x+5$, find the point where the ordinate $y$ increases 5 times faster than the abscissa $x$.
Solution. We find the derivative $y^{\prime}=2 x-3$ (see the solution of the previous example). Since the derivative characterizes the rate of change of the ordinate $y$ compared to the change in the abscissa $x$, from the condition $y^{\prime}=2 x-3=5$ we find the abscissa of the desired point: $x=4$. We find the ordinate from the equation of the curve: $y=4^{2}-3 \cdot 4+5=9$. Thus, $(4 ; 9)-$ is the desired point.