5. MAXIMA AND MINIMA
DEFINITION :
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.
6.
7. 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.
20. 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).
21. 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.
22. 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.
