Question

question 1 - 19
the function ( h(x)=-0.0005(x - 1905)^{2}+310 ) models the horsepower at the wheels of a vehicle with a poorly maintained diesel engine as a function of the engine speed ( x ), in revolutions per minute (rpm), where ( 1600leq xleq2100 ).
what is the engine speed, in rpm, at which the vehicles estimated horsepower at the wheels is greatest?
rpm

Explanation:

Step1: Analyze the function form

The function \(H(x)=- 0.0005(x - 1905)^{2}+310\) is in the vertex form of a parabola \(y = a(x - h)^{2}+k\), where \(a=-0.0005\), \(h = 1905\), and \(k = 310\).

Step2: Determine the vertex properties

Since \(a=-0.0005<0\), the parabola opens downwards. The vertex of the parabola \((h,k)\) gives the maximum value of the function.

Answer:

\(1905\)