Applications Of Derivatives Question 99

Question: The function $ f(x)=\tan x-x $

[MNR 1995; Pb. CET 2000; Karnataka CET 2002]

Options:

A) Always increases

B) Always decreases

C) Never decreases

D) Sometimes increases and sometimes decreases

Show Answer

Answer:

Correct Answer: A

Solution:

$ y=\tan x-x\Rightarrow \frac{dy}{dx}={{\sec }^{2}}x-1={{\tan }^{2}}x\ge 0 $ .