Application of Derivatives

Introduction:
Differential calculus can be considered as mathematics of motion, growth and change where there is a motion, growth, change. Whenever there is variable forces producing acceleration, differential calculus is the right mathematics to apply.
Let us began this chapter with the following statement:

• Often a physician may want to test how small changes in dosage can affect the body's response to a particular drug.

• An economist may want to study how investment changes with variation in interest rates.

• How the velocity of a heavy meteorite entering the earth's surface, changes with its distance from the earth's surface.

• For a given volume of oil, what is the least expensive shape of an oil can?

Differential calculus can be considered as mathematics of motion, growth and change where there is a motion, growth, change. Whenever there is variable forces producing acceleration, differential calculus is the right mathematics to apply. Application of derivatives are used to represent and interprete the rate at which quantities change with respect to another variable. Most of the changes are considered in terms of independent variable time. But there is no restriction that the changes are considered with respect to time only, as we have seen in the above mentioned, statements.