[tex]y=x^2-120x+5000[/tex][tex]\begin{gathered} \text{Applying the knowledge of turning points of quadratic function} \\ at\text{ turning point, slope }\frac{d\text{y}}{d\text{x}}\text{ = 0} \end{gathered}[/tex][tex]\begin{gathered} \frac{d\text{ y}}{d\text{ x}}\text{ = 2x-120 = 0} \\ \\ 2x\text{ - 120 = 0} \\ 2x\text{ = 120} \\ x=\frac{120}{2} \\ x=\text{ 60} \end{gathered}[/tex]
The cruising speed that minimizes the cost is 60 mph
