Question

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 :

In an agricultural institute, scientists do experiments with varieties of seeds to grow them in different environments to produce healthy plants and get more yield. A scientist observed that a particular seed grew very fast after germination. He had recorded growth of plant since germination and he said that its growth can be defined by the function f(x) = (1/3)x³ - 4x² + 15x + 2, 0 ≤ x ≤ 10 where x is the number of days the plant is exposed to sunlight. On the basis of the above information, answer the following questions :