Question

Overspeeding increases fuel consumption and decreases fuel economy as a result of tyre rolling friction and air resistance. While vehicles reach optimal fuel economy at different speeds, fuel mileage usually decreases rapidly at speeds above 80 km/h. The relation between fuel consumption F (l/100 km) and speed V (km/h) under some constraints is given as F = V²/500 – V/4 + 14. On the basis of the above information, answer the following questions :

If the sides of a square are decreasing at the rate of 1·5 cm/s, the rate of decrease of its perimeter is :

Find the intervals in which the function f(x) = log x/x is strictly increasing or strictly decreasing.

Find the absolute maximum and absolute minimum values of the function f given by f(x) = x/2 + 2/x, on the interval [1, 2].