Question

In order to set up a rain water harvesting system, a tank to collect rain water is to be dug. The tank should have a square base and a capacity of 250 m³. The cost of land is ₹ 5,000 per square metre and cost of digging increases with depth and for the whole tank, it is ₹ 40,000 h², where h is the depth of the tank in metres. x is the side of the square base of the tank in metres.

A volleyball player serves the ball which takes a parabolic path given by the equation h(t) = −(7/2)t² + (13/2)t + 1, where h(t) is the height of ball at any time t (in seconds), (t ≥ 0).

Find the maximum and minimum values of the function given by f(x) = 5 + sin 2x.

The median of an equilateral triangle is increasing at the rate of 2√3 cm/s. Find the rate at which its side is increasing.