Question

AUTOMOBILES The engine torque y (in foot-pounds) of one model of car is given by y = º3.75x2 + 23.2x + 38.8 where x is the speed of the engine (in thousands of revolutions per minute). Find the engine speed that maximizes torque. What is the maximum torque?

Answer 1

Part 1) The engine speed that maximizes torque is
`3,093 rev/min`

Part 2)The maximum torque is
`74.683\ foot-pounds`

Explanation:

The correct equation is

`y=-3.75x^(2)+23.2x+38.8`

This is the equation of a vertical parabola open downward (because the leading coefficient is negative)

The vertex represent a maximum

The x-coordinate of the vertex represent the engine speed that maximizes torque

The y-coordinate of the vertex represent the maximum torque

Solve the quadratic equation by graphing

using a graphing tool

The vertex is the point (3.093,74.683)

see the attached figure

therefore

The engine speed that maximizes torque is

`3.093(1,000)=3,093 rev/min` ---> because is in thousands of revolutions per minute

The maximum torque is

`74.683\ foot-pounds`