Which of the following function is increasing for all values of x in the domain (0, ∞) ?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $x|x|$
$f(x)=x|x|$
for $x>0$,
$f(x)=x^2$
and,
$f'(x)=2x>0$ $(\forall x>0)$
∴ $x|x|$ is increasing function in $(0, ∞)$.