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