Maharashtra Board Solutions for Chapter: Applications of Derivatives, Exercise 4: EXERCISE 2.4

A ball is thrown in the air. Its height at any time $t$ is given by $h=3+14t-5t^2$. Find the maximum height it can reach.

The perimeter of a triangle is $10 \mathrm{cm}$. If one of the side is $4 \mathrm{cm}$. What are the other two sides of the triangle for its maximum area?

A box with a square base is to have an open top. The surface area of the box is $192\mathrm{sq}.\mathrm{cm}$. What should be its dimensions in order that the volume is largest ?

The profit function $P\left(x\right)$ of a firm, selling $x$ items per day is given by $P\left(x\right)=\left(150-x\right)x-1625$. Find the number of items the firm should manufacture to get maximum profit. Find the maximum profit.

Find two numbers whose sum is $15$ and when the square of one multiplied by the cube of the other is maximum.

Show that among rectangles of given area, the square has the least perimeter.

Show that the height of a closed right circular cylinder of a given volume and least surface area is equal to its diameter.

Find the volume of the largest cylinder that can be inscribed in a sphere of radius '$r$' $\mathrm{cm}$.