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 :

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CASE_STUDIESDerivative as Rate of ChangeApplications of Derivatives in Rate of Change ProblemsLocal Maxima and Local MinimaCBSE PYQ3 sub-questions

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Show that the function f(x) = 4x³ – 18x² + 27x – 7 has neither maxima nor minima.

TextLocal Maxima and Local MinimaFirst Derivative Test for Maxima and Minima

The traffic police has installed Over Speed Violation Detection (OSVD) system at various locations in a city. These cameras can capture a speeding vehicle from a distance of 300 m and even function in the dark. A camera is installed on a pole at the height of 5 m. It detects a car travelling away from the pole at the speed of 20 m/s. At any point, x m away from the base of the pole, the angle of elevation of the speed camera from the car C is θ. On the basis of the above information, answer the following questions :

CASE_STUDIES