A housing society wants to commission a swimming pool for its residents. For this, they have to purchase a square piece of land and dig this to such a depth that its capacity is 250 cubic metres. Cost of land is ₹ 500 per square metre. The cost of digging increases with the depth and cost for the whole pool is ₹ 4000 (depth)². Suppose the side of the square plot is x metres and depth is h metres. On the basis of the above information, answer the following questions :

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CASE_STUDIESApplications of Derivatives in Rate of Change ProblemsSecond Derivative Test for Maxima and MinimaCBSE PYQ3 sub-questions

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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_STUDIESDerivative as Rate of ChangeApplications of Derivatives in Rate of Change Problems

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 :

CASE_STUDIESDerivative as Rate of ChangeApplications of Derivatives in Rate of Change ProblemsLocal Maxima and Local Minima