This document discusses differential calculus, a branch of mathematics focused on derivatives and differentials, and its applications in everyday life, including business and engineering. It includes examples such as calculating fuel efficiency in cars and maximizing the product of two positive numbers under certain conditions. The document emphasizes the importance of understanding rates of change, which can be visually represented through graphs and calculated using derivatives.

1. By Ebin Robinson
AS Level
IN721
LIC

2. It is a branch of mathematics concerned with the
determination, properties, and application of derivatives
and differentials.

3. Differential calculus is being applied in our day to day life~
it is being involved in doing business, engineering and what
even driving.
Below we can see a few examples.

4. You can calculate the amount of fuel used by a car. So that
it makes you convineient to know that in which speed it
takes the least amount of fuel. So that you can drive
conservatively.
The fuel used by a car is defined by f(v)=3/80v2−6v+245,
where v is the travelling speed in km/h.

5. The sum of two positive numbers is 10. One of the
numbers is multiplied by the square of the other. If each
number is greater than 0, find the numbers that make this
product a maximum.
How do you do this????

8. It is vey useful to determine how fast (the rate at which)
things are changing. Mathematically we can represetn
change in different ways. For example we can use
algebraic formulae or graphs.Graphs give a visual
representation of the rate at which the function values
change as the independent (input) variable changes. This
rate of change is described by the gradient of the graph
and can therefore be determined by calculating the
derivative.