QJEEM19Ma5085: JEE Main 2019 Mathematics - Class 12 JEEM19Ma5085 Solution: Let f(x) = x a 2 + x 2 − d − x b 2 + ( d − x ) 2 , x ∈ R, where …

Question

Verified Solution • 2025–26 Session moderate

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 :

Accepted Answer

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

f^{'} (x) = \frac{a^{2}}{{(a^{2} + x^{2})}^{3 / 2}} + \frac{b^{2}}{{(b^{2} + {(d - x)}^{2})}^{3 / 2}} > 0 \forall x \in R

f(x) is an increasing function.

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