Question

If M and m denote the local maximum and local minimum values of the function f(x) = x + 1/x (x ≠ 0) respectively, find the value of (M – m).

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 :

It is given that function f(x) = x⁴ – 62x² + ax + 9 attains local maximum value at x = 1. Find the value of 'a', hence obtain all other points where the given function f(x) attains local maximum or local minimum values.