spain-selectividad 2023 QA.2

spain-selectividad · Other · selectividad__madrid_matematicas-II_extraordinaria 2 marks Stationary points and optimisation Find absolute extrema on a closed interval or domain
A team of engineers conducts fuel consumption tests for a new hybrid vehicle. The fuel consumption in liters per 100 kilometers as a function of speed, measured in tens of kilometers per hour, is
$$c ( v ) = \left\{ \begin{array} { l l l } \frac { 5 v } { 3 } & \text { if } & 0 \leq v < 3 \\ 14 - 4 v + \frac { v ^ { 2 } } { 3 } & \text { if } & v \geq 3 \end{array} \right.$$
a) (1 point) If in a first test the vehicle must travel at more than 3 tens of kilometers per hour, at what speed should the vehicle travel to obtain minimum fuel consumption?\ b) (1.5 points) If in another test the vehicle must travel at a speed $v$ such that $1 \leq v \leq 8$, what will be the maximum and minimum possible fuel consumption of the vehicle?
A team of engineers conducts fuel consumption tests for a new hybrid vehicle. The fuel consumption in liters per 100 kilometers as a function of speed, measured in tens of kilometers per hour, is

$$c ( v ) = \left\{ \begin{array} { l l l } 
\frac { 5 v } { 3 } & \text { if } & 0 \leq v < 3 \\
14 - 4 v + \frac { v ^ { 2 } } { 3 } & \text { if } & v \geq 3
\end{array} \right.$$

a) (1 point) If in a first test the vehicle must travel at more than 3 tens of kilometers per hour, at what speed should the vehicle travel to obtain minimum fuel consumption?\
b) (1.5 points) If in another test the vehicle must travel at a speed $v$ such that $1 \leq v \leq 8$, what will be the maximum and minimum possible fuel consumption of the vehicle?