Applications of First Derivative
Applications of First Derivative: Overview
This Topic covers sub-topics such as Monotonicity of a Function, Stationary Points, Maxima and Minima of a Function, Local Maximum and Minimum of a Function and, Global Maximum and Minimum of a Function
Important Questions on Applications of First Derivative
The values of at the stationary points of are

A wire of length is cut into two parts. One part is bent into a circle and other into a square. Sum of the areas of the circle and the square is the least, if the radius of the circle is , where is the radius of circle. Find .

Find the value of , if the co-ordinate of the point on the curve which are nearest to the point is .

A manufacturer can sell items at the rate of each. The cost of producing items is . How many items must be sold so that his profit is maximum.

An open cylindrical tank whose base is a circle is to be constructed of metal sheet so as to contain a volume of cu.cm of water. Find the dimensions(in cm) so that the quantity of metal sheet required is a minimum.

A telephone company in the town has subscribers on its list and collects fixed rent charges of per year from each person. The company proposes to increase annual rent and it is believed that for every increase of rupee in the rent one subscriber will be discontinued. Find what increased annual rental (in Rs.) will bring the maximum annual income to the company.

A rectangular sheet of paper has the area sq. meters. The margin at the top and bottom is and sides each. If the length and breadth of the paper is , then find the value of , if the area of the printed space is maximum?

What is the area of the largest size of a rectangle that can be inscribed in a semicircle of radius unit, so that two vertices lie on the diameter.

A metal wire of long is bent to form a rectangle. Let its length and breadth be , then find value of , when its area is maximum.

If ([•] denotes the greatest integer function) and is non-constant continuous function, then:

A metal wire of long is bent to form a rectangle. Let its length and breadth be , then find value of , when its area is maximum.

If the minimum value of the function is , then value of is

If the maximum and minimum value of the function is then find the value of .

Find the value of , if is a decreasing function for .

Find the value of , if is an increasing function for .

Find the value of , if is a decreasing function for .

Find the values of , if is an increasing function in the interval .

Find the values of such that is a decreasing function.

Find the values of such that is a decreasing function.

Find the values of such that is an increasing function.
