Applications of First Derivative

IMPORTANT

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

EASY
IMPORTANT

The values of x at the stationary points of fx=x3+3x2-2 are

HARD
IMPORTANT

A wire of length l  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 rk, where r is the radius of circle. Find k.

HARD
IMPORTANT

Find the value of k, if the co-ordinate of the point on the curve 4y=x2 which are nearest to the point (0,5) is ±2k,3.

HARD
IMPORTANT

A manufacturer can sell x items at the rate of (330-x) each. The cost of producing x items is x2+10x+12. How many items must be sold so that his profit is maximum.

HARD
IMPORTANT

An open cylindrical tank whose base is a circle is to be constructed of metal sheet so as to contain a volume ofπa3 cu.cm of water. Find the dimensions(in cm) so that the quantity of metal sheet required is a minimum.

HARD
IMPORTANT

A telephone company in the town has 5000 subscribers on its list and collects fixed rent charges of Rs 3000 per year from each person. The company proposes to increase annual rent and it is believed that for every increase of 1 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.

MEDIUM
IMPORTANT

A rectangular sheet of paper has the area 24 sq. meters. The margin at the top and bottom is 75 cm and sides 50 cm each. If the length and breadth of the paper is a m, b m, then find the value of ab, if the area of the printed space is maximum?

HARD
IMPORTANT

What is the area of the largest size of a rectangle that can be inscribed in a semicircle of radius 1 unit, so that two vertices lie on the diameter.

MEDIUM
IMPORTANT

A metal wire of 36cm long is bent to form a rectangle. Let its length and breadth be m, n, then find value of m+n, when its area is maximum.

MEDIUM
IMPORTANT

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

MEDIUM
IMPORTANT

A metal wire of 36cm long is bent to form a rectangle. Let its length and breadth be m, n, then find value of m+n, when its area is maximum.

MEDIUM
IMPORTANT

If the minimum value of the function f(x)=x2+16x2 is m, then value of m is

MEDIUM
IMPORTANT

If the maximum and minimum value of the function f(x)=2x3-21x2+36x-20 is m,n then find the value of m+n.

MEDIUM
IMPORTANT

Find the value of m, if f(x)=xx2+1 is a decreasing function for x(-,-m]  [m,).

MEDIUM
IMPORTANT

Find the value of m+n, if f(x)=xx2+1 is an increasing function for xm,n.

MEDIUM
IMPORTANT

Find the value of m+n, if f(x)=2x3-15x2-144x-7 is a decreasing function for xm,n.

MEDIUM
IMPORTANT

Find the values of m+n, if f(x)=2x3-15x2-144x-7 is an increasing function in the interval (-, -m]  [n, ).

MEDIUM
IMPORTANT

Find the values ofx, such that f(x)=2x3-15x2-84x-7 is a decreasing function.

MEDIUM
IMPORTANT

Find the values of such that f(x)=x4-2x3+1 is a decreasing function.

MEDIUM
IMPORTANT

Find the values of x, such that f(x)=x2+2x-5 is an increasing function.