Differential Calculus for CBSE & Bihar Board and also important for all State Board

 

in this Post i will Discussed about unit third that is Calculus ( especially Differential Calculus ) so the syllabus of  of Differential calculus is

in this blog i'm going to discussed about Application of Differential calculus. but before studying this I'm going to give a brief introduction of some basic and important topics of differential calculus. if you have already know the concepts of all these topic then you can easily understand application of Derivative Part

all the above topics are the fundamental topic of Differential calculus and after that know you are able o Understand the real life applications of Differential Calculus. so following Tonics are important for 12th Levels and IIT-JEE points of View but in 12th CBSE Board Points of View only Three Topics are Important.

Rate of Change and Approximations' are Delated according to new syllabus of CBSE first term, that's why today I'm Going to start with Increasing and Decreasing 

Before understanding the Concepts of Increasing and Decreasing. First of all we have to need the knowledge the basic concepts of Intervals and sign Scheme. S now lets get start the Discussion about Intervals and sign-Scheme

i hope now you understand the Geometrical meaning of inequality and concepts of intervals. now we try to understand the basic Rule of Sign- Scheme

How to solve this Type of Problems and how to identify which interval's Functions are positive or Negative?

 Rule of Sign Scheme for rational/polynomials Function 
 1 Put Numerator and Denominators equal to zero, Separately and then find roots

2 plot a number line. Mark these points(roots) on the number line in terms o Their Increasing order

3 the whole number line is divided in to a subintervals

4 now if root is repeated even times the sign of the function will remain the same in the two adjacent sub-intervals of root but if repeated odd times then sign will be changes