CALCULUSPRACTICLE APPLICATION OF

MAXIMA AND MINIMA

GROUP MEMBERS

HAMZA SHAUKAT

I.A.S DEPARTMENT PUNJAB UNIVERSITY

LAHORE PAKISTAN

MAXIMA AND

MINIMA

MAXIMA AND MINIMA

The maximum of a function is the highest value

that it reaches over a closed interval.

Similarly, the minimum of a function is the lowest

value that it reaches over a closed interval.

DEFINITION :

HOW TO FIND MAXIMA AND MINIMA

EXAMPLE

Find maxima or minima of following function

F (x) = x² - 6x +1

Taking first derivative

F (x) = 2x – 6 = 0

2x = 6

X = 3

Now take the second derivative

F (x) = 2 > 0

So the function is at minima when x =3. After

x = 3 function starts increasing so at x = 3

function is at minimum point.

PRACTICLE APPLICATION OF MAXIMA AND MINIMA

EXAMPLE NO 1

The profit function of acrosonic company is given by

SOLUTION

EXAMPLE NO 2

An economy’s consumer price index (CPI) is

described by the function.

SOLUTION

EXAMPLE NO 3

Find the dimension of rectangle fence of

length 100 ft that maximize the area ?

SOLUTION

ANSWER

X = 50 ft AND Y = 25 ft

EXAMPLE NO 4

Find where to cut the wire of the

length 12 inches such that the sum

of area of the square and circle is

minimize ?

SOLUTION

PRACTICLE APPLICATION OF MAXIMA AND MINIMA

PRACTICLE APPLICATION OF MAXIMA AND MINIMA

In CHEM , we have used the maxima of wave function and

radial probability distribution functions to

determine where an electron is most likely

to be found in any given orbital.

In PHYS, the maximum (or minimum) displacement of a

wave is known as its amplitude, and is occasionally found

graphically. We have also solved equations to determine the

maxima of velocity and acceleration functions for waves,

using other physical principles (such as the Law of

Conservation of Energy).

In Economics maxima and minima are used to maximize

beneficial values (profit, efficiency, output, etc.) and to

minimize negative ones (expenses, effort, etc.).

A meteorologist creates a model that predicts temperature

variance with respect to time. The absolute maximum and

minimum of this function over any 24-hour period are the

forecasted high and low temperatures.

The director of a theme park works with a model of total

revenue as a function of admission price. The location of the

absolute maximum of this function represents the ideal

admission price (i.e., the one that will generate the most

revenue).

A NASA engineer working on the next generation space

shuttle studies a function that computes the pressure acting

on the shuttle at a given altitude. The absolute maximum of

this function represents the pressure that the shuttle must

be designed to sustain.

QUESTIONSNOW