State whether f(x)= -x is increasing or decreasing its domain. - Vidyadip

Question

State whether $\text{f}(\text{x})=\tan\text{x}-\text{x}$ is increasing or decreasing its domain.

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Answer

$\text{f}(\text{x})=\tan\text{x}-\text{x}$

$\text{f}'(\text{x})=\sec^2\text{x}-1$

$\tan^{2}\text{x}\geq0,\forall\ \text{x}\in[0,2\pi]$

So, f(x) is increasing in its domain.

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