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Which of the following function is increasing for all values of x in the domain (0, ∞) ? |
$1-x^2$ $\frac{1}{x}$ $8-x^2$ $x|x|$ |
$x|x|$ |
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 $(0, ∞)$. |
