Question

The function f(x) = x³ – 3x² + 12x – 18 is :

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).

Show that f(x) = eˣ – e⁻ˣ + x – tan⁻¹ x is strictly increasing in its domain.

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 :