Question

Let $ f(x) = \sin x - \tan x $ , $ x \in (0,\pi/2) $ , then tangent drawn to the curve $ y = f(x) $ at any point will

• A. lie above the curve
• B. lie below the curve
• C. Nothing can be said
• D. be parallel to a fixed line

Answer 1

Answer: (A)

Given, $ y=\sin x-\tan x$
$\Rightarrow \frac{d y}{d x} =\cos x-\sec ^{2} x $
$\Rightarrow \frac{d^{2} y}{d x^{2}} =-\sin x-2 \sec ^{2} x \tan x< 0, $
$ \forall x \in(0, \pi / 2)$
Hence, the tangent drawn to the curve will lie above the curve.