Answer:
The rate of change of the number of vehicles waiting with respect to the traffic intensity for the intensities are:
a) 0.52
b) 2.63
Step-by-step explanation:
The rate of change of a function at a given point P can be obtained by evaluating the 1st derivative of the function in P. Thus,
[tex]f(x)=\frac{x^2}{2(1-x)}[/tex]
[tex]\frac{df(x)}{dx} = \frac{d(\frac{x^2}{2(1-x)})}{dx} \\\frac{df(x)}{dx} =\frac{x}{1-x} + \frac{x^2}{2(1-x)^2} \\\frac{df(x)}{dx} = -\frac{x(x-2)}{2(x-1)^2}[/tex]
Now for we just need to evaluate in each of the given points
a) [tex]\frac{df(0.3)}{dx} =-\frac{0.3(0.3-2)}{2(0.3-1)^2}\\\boxed{\frac{df(0.3)}{dx} =0.520408 \approx 0.52}[/tex]
b)[tex]\frac{df(0.6)}{dx} =-\frac{0.6(0.6-2)}{2(0.6-1)^2}\\\boxed{\frac{df(0.6)}{dx} = 2.625\approx 2.63}[/tex]
