There are many extensive topics to cover from the Maths CBSE Class 12 syllabus. Students have to develop extra attentiveness while practising the chapters of Maths because of the **Maths Class 12 Chapter wise weightage** which plays a very important role in the final exam. Extramarks provides the best quality learning material for Maths syllabus for Class 12 CBSE which is kept on par with the new **pattern for CBSE Class 12 Mathematics**. Below are some of the important topics from the CBSE Class 12 Mathematics syllabus.

Chapter 1 Relations and Functions

Chapter 2 Inverse Trigonometric Functions

Chapter 3 Matrices

Chapter 4 Determinants

Chapter 5 Continuity and Differentiability

Chapter 6 Application of Derivatives

Let x be a point in the domain of definition of a real-valued function f, then f is said to be increasing, strictly increasing, decreasing or strictly decreasing at x, if there is an open interval I containing x, such that f is increasing, strictly increasing, decreasing or strictly decreasing, respectively, in I.

Note: If for a given interval I allow R, function f increases for some values in I and decreases for other values in I, then we say a function is neither increasing nor decreasing.

Let f be continuous on [ a, b] and separated on an open interval (a, b). Second Derivative Test: let f(x) be a function defined at an interval I and c at interval I. Let f be two times differentiable to c. Then Ix= c is a local maxima point, if f'(c)=0 and f'(c) is <0. (ii)x= c is a local minima point, if f'(c)=0 and f'(c) is > 0.

(iii) the test fails if f'(c)=0 and f'(c)=0.

Note I If the test fails, we will go back to the first derivative test and find out whether a is a local maxima point, a local minimum or a point of inflexion.

(ii) If we say that f is twice differentiable at o, then that means that a second-order derivative exists at a.

Absolute Maximum Value: let f(x) be a function defined in its domain, say Z to R. Then f(x) is said to have the maximum value at a point where Z is real, if f(x) ≤ f(a) is valid, and Z is valid.

Absolute Minimum Value: let f(x) be a function defined in its domain, say z by R. Then f(x) is said to have the minimum value at a point where Z is valid, if f(x) ≥ f(a) is valid, and Z is valid.

Note: Every continuous function specified in a closed range has a maximum or minimum value, either at the endpoint or at the solution of f'(x)= 0 or at the point where the function can not be distinguished.

Let f be a continuous function at interval I=[ a, b]. Then f has the absolute maximum value, and/or at least once in I. Additionally, f has the absolute minimum value, which is reached at least once in I.

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