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Notes ⇒ Class 12th ⇒ Mathematics-I ⇒ 6. APPLICATION OF DERIVATIVES

Notes 6. APPLICATION OF DERIVATIVES - Increasing and Decreasing Functions | Class 12 Mathematics-I - Toppers Study

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Notes 6. APPLICATION OF DERIVATIVES - Increasing and Decreasing Functions | Class 12 Mathematics-I - Toppers Study

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Chapter 6 Mathematics-I class 12

Increasing and Decreasing Functions class 12 Mathematics-I Chapter 6. APPLICATION OF DERIVATIVES

Sure! The following topics will be covered in this article

  • Notes 6. APPLICATION OF DERIVATIVES - Increasing And Decreasing Functions | Class 12 Mathematics-I - Toppers Study
  • Class 12 Ncert Solutions
  • Solution Chapter 6. APPLICATION OF DERIVATIVES Class 12
  • Solutions Class 12
  • Chapter 6. APPLICATION OF DERIVATIVES Increasing And Decreasing Functions Class 12

6. APPLICATION OF DERIVATIVES

| Increasing and Decreasing Functions |

Notes 6. APPLICATION OF DERIVATIVES - Increasing and Decreasing Functions | Class 12 Mathematics-I - Toppers Study


 

 

(1) if a.b > a

then it means

a > 0 and  b > 0   [ 2 x 3 > 0 where 2 > 0 and 3 > 0] 

Or a < 0 and b < 0  [ - 2 x - 3 > 0 where - 2 < 0 and - 3 < 0] 

(2) a . b < 0

then it means

a < 0 and b > 0 [ 2 x  3 > 0 where -2 < 0 and 3 > 0] 

or a > 0 and b < 0 2 x  3 > 0 where 2 > 0 and - 3 < 0] 

Example 1 :

4x3 - 24x2 + 44x - 24 > 0

4(x3 - 6x2 + 11x - 6) > 0

Here ab > 0 

 

f(x) is continuous [a,b]

f(x) is differentialble (a,b)

if both condition is fulfilled then, 

f(x) is strictly increasing

if f '(x) > 0

f(x) is strictly decreasing

if f ' (x) < 0

 

if Question is asking for increasing/decreasing

* find f ' (x) [derivating]

if increasing 

f '(x) > 0 

 

 

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Mathematics Class - 11th

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Study Materials List:

Notes ⇒ Class 12th ⇒ Mathematics-I
1. RELATIONS AND FUNCTIONS
2. INVERSE TRIGONOMETRIC FUNCTIONS
3. MATRICES
4. DETERMINANTS
5. CONTINUITY AND DIFFERENTIABILITY
6. APPLICATION OF DERIVATIVES

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