CBSE Class 11-Mathematics: Mathematics Revision Sheet for Class 11 and Class 12 Physics
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April 9, 2012
Differentiation
We have two quantities and such that where is some function of . We may be interested in finding followings things
1.
2. Maximum and Minimum values of y. It can be finding with the method of Maxima and Minima
Is the called the derivative of y w.r.t to
It is defined as
Some commonly known functions and their derivatives are: -
Some important and useful rules for finding derivatives of composite functions
1. where c is constant
2. where a and b are function of
3.
4.
5.
6.
Maximum and Minimum values of
Step 1:
Fine the derivative of
Step2:
Equate
Solve the equation to find out the values of
Step3:
Find the second derivative of and calculate the values of
for the values of from step 2
If then the value of x corresponds to mimina of y then then can be find out by putting this value of
If then the value of corresponds to maxima of then can be find out by putting this value of
Integration
It reads as integration of function f(x) w.r.t. x within the limits from x=a to x=b.
Integration of some important functions are
Useful rules for integration are