Dogde Caliber

The petrol kilometers M (unit: kilometers per liter) of the Dodge Caliber car is modeled by the function:

$M(s)=-1/28s^2+3s-31$

What is the car's best petrol kilometers, and what speed is attained?

Correct answer:

M =  32 km/l
s =  42 km/h

Step-by-step explanation:

$$\begin{gathered} M(s)=-1/28s^2+3s-31 \\ {M}^{\prime }=\frac{dM(s)}{s}=-2/28s+3 \\ {M}^{\prime }=0 \\ -2/28s+3=0 \\ s=3\cdot 28/2=42\text{km/h} \\ M=-1/28\cdot s^2+3\cdot s-31=-1/28\cdot 42^2+3\cdot 42-31=32\text{km/l} \end{gathered}$$

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