The function f defined by
is:
increasing in R.
decreasing in R.
decreasing in (0, ∞) and increasing in (−∞, 0).
increasing in (0, ∞) and decreasing in (−∞, 0).
As we learnt in
Condition for increasing functions -
For increasing function tangents drawn at any point on it makes an acute slope with positive x-axis.
- wherein
Where f(x) is continuous for (a,b)
So,
for
Correct option is 1.
Option 1)
increasing in R.
This option is incorrect.
Option 2)
decreasing in R.
This option is incorrect.
Option 3)
decreasing in (0, ∞) and increasing in (−∞, 0).
This option is correct.
Option 4)
increasing in (0, ∞) and decreasing in (−∞, 0).
This option is incorrect.