Question

5) Bob is driving to grandma's house in Duluth for Thanksgiving. The following quadratic equation is the fuel cost of driving Bob's car on the highway at speed x. Find the cruising speed that minimizes the driving cost (x is speed in mph & yis cost in cents). y=x2-120x + 5000

Answer 1

`y=x^2-120x+5000`
`\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}`
`\begin{gathered} \frac{d\text{ y}}{d\text{ x}}\text{ = 2x-120 = 0} \\ \\ 2x\text{ - 120 = 0} \\ 2x\text{ = 120} \\ x=(120)/(2) \\ x=\text{ 60} \end{gathered}`

The cruising speed that minimizes the cost is 60 mph