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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
The curve $y=\frac{x}{1+x\tan x}$ attains maxima
Solution
Given the curve$y = \dfrac{x}{1 + x \tan x}$
Differentiate using quotient rule:
$y' = \dfrac{(1 + x \tan x) - x(\tan x + x \sec^2 x)}{(1 + x \tan x)^2}$
Simplify the numerator:
$N = 1 + x \tan x - x \tan x - x^2 \sec^2 x$
$N = 1 - x^2 \sec^2 x$
Set $N = 0$ for maxima/minima:
$1 - x^2 \sec^2 x = 0$
$x^2 \sec^2 x = 1$
$x \sec x = \pm 1$
Hence the curve attains maxima when:
$x \sec x = 1$
$x=\cos x$
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