(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