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The function $f(x) = \tan x - x$ |
always increases always decreases never increases sometimes increases and sometimes decreases |
always increases |
The correct answer is Option (1) → always increases ## We have, $f(x) = \tan x - x$ $∴f'(x) = \sec^2 x - 1 \quad [∵\sec^2 x \in [1, \infty)]$ $\Rightarrow f'(x) > 0, \forall x \in R$ So, $f(x)$ always increases. |
