Question:
Let $f(x)=\frac{x}{\sqrt{a^{2}+x^{2}}}-\frac{d-x}{\sqrt{b^{2}+(d-x)^{2}}}, \quad x \in R$,
where a, b and d are non-zero real constants. Then :-
Correct Option: , 4
Solution:
$f(x)=\frac{x}{\sqrt{a^{2}+x^{2}}}-\frac{d-x}{\sqrt{b^{2}+(d-x)^{2}}}$
$f^{\prime}(x)=\frac{a^{2}}{\left(a^{2}+x^{2}\right)^{3 / 2}}+\frac{b^{2}}{\left(b^{2}+(d-x)^{2}\right)^{3 / 2}}>0 \forall x \in R$
$f(x)$ is an increasing function.