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.

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CASE_STUDIESApplications of Derivatives in Rate of Change ProblemsFirst Derivative Test for Maxima and MinimaSecond Derivative Test for Maxima and MinimaAbsolute Maximum and Absolute Minimum Values4 sub-questions

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

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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 :

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