Chapter-6. Application of Derivatives Mathematics-I class 12 in english Medium CBSE Notes

(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