jee-advanced 2007 Q60

jee-advanced · India · paper1 Stationary points and optimisation Determine intervals of increase/decrease or monotonicity conditions

Let $f(x) = \frac{x}{\sqrt{a^2+x^2}} - \frac{d-x}{\sqrt{b^2+(d-x)^2}}$, where $a$, $b$, and $d$ are positive constants. Then
(A) $f$ is an increasing function of $x$
(B) $f$ is a decreasing function of $x$
(C) $f$ is neither increasing nor decreasing function of $x$
(D) $f'$ is not a monotonic function of $x$

Let $f(x) = \frac{x}{\sqrt{a^2+x^2}} - \frac{d-x}{\sqrt{b^2+(d-x)^2}}$, where $a$, $b$, and $d$ are positive constants. Then\\
(A) $f$ is an increasing function of $x$\\
(B) $f$ is a decreasing function of $x$\\
(C) $f$ is neither increasing nor decreasing function of $x$\\
(D) $f'$ is not a monotonic function of $x$

Paper Questions

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