Table of Contents
NCERT Solutions for Application of Derivatives Class 12 Notes Maths Chapter 6
Question 1
A particle moves along a straight line. Its position at time t is s(t) metres from the origin.
(i) Find the velocity of the particle at time t.
(ii) Find the acceleration of the particle at time t.
Solution:
(i) Velocity of the particle at time t is given by
v(t) = ds/dt
= (s(t+h) – s(t))/h
= (s(t+h) – s(t))/h
(ii) Acceleration of the particle at time t is given by
a(t) = dv/dt
= (v(t+h) – v(t))/h
= (v(t+h) – v(t))/h
Maximum and Minimum Value
of a Function
The maximum value of a function is the largest value that the function can take on, while the minimum value of a function is the smallest value that the function can take on.
For example, consider the function f(x) = x2. The maximum value of this function is x = √(2) = 2, and the minimum value is x = -√(2) = -2.
Important Points of Applications of Derivatives
The most important application of derivatives is in the field of finance. Derivatives are used to manage financial risks. For example, a company might use derivatives to protect itself from the risk of a sudden change in interest rates.
Derivatives are also used in the stock market. Investors use derivatives to make bets on the movement of stock prices.
Derivatives are also used to create financial instruments called derivatives contracts. These contracts are used to transfer the risk of an investment from one party to another.
