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:Part 1) The engine speed that maximizes torque is [tex]3,093 rev/min[/tex]Part 2)The maximum torque is [tex]74.683\ foot-pounds[/tex]Step-by-step explanation:The correct equation is[tex]y=-3.75x^{2}+23.2x+38.8[/tex]This is the equation of a vertical parabola open downward (because the leading coefficient is negative)The vertex represent a maximumThe x-coordinate of the vertex represent the engine speed that maximizes torqueThe y-coordinate of the vertex represent the maximum torqueSolve the quadratic equation by graphingusing a graphing toolThe vertex is the point (3.093,74.683)see the attached figurethereforeThe engine speed that maximizes torque is [tex]3.093(1,000)=3,093 rev/min[/tex] ---> because is in thousands of revolutions per minuteThe maximum torque is [tex]74.683\ foot-pounds[/tex]