Let f(x) = where a, b and d are non-zero real constants. Then:

Engineering

Mathematics

Monotonicity

Question

Let f(x) = $\frac{x}{\sqrt{a^{2} + x^{2}}} - \frac{d - x}{\sqrt{b^{2} + {(d - x)}^{2}}}, x \in R$ where a, b and d are non-zero real constants. Then:

f is neither increasing nor decreasing function of x

f ' is not a continuous function of x

f is an increasing function of x

f is a decreasing function of x

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$f (x) = \frac{x}{\sqrt{a^{2} + x^{2}}} - \frac{d - x}{\sqrt{b^{2} + {(d - x)}^{2}}}$

$f (x) = \frac{x}{\sqrt{a^{2} + x^{2}}} + \frac{x - d}{\sqrt{b^{2} + {(x - d)}^{2}}}$

= sin tan^{– 1} $\frac{x}{a}$ + sin tan^{– 1} $\frac{x - d}{b}$

⇒ f (x) is an increasing function