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Question
The interval of increase of the function f(x) = x − ex + tan (2π/7) is
Options
(0, ∞)
(−∞, 0)
(1, ∞)
(−∞, 1)
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Solution
(−∞, 0)
\[f\left( x \right) = x - e^x + \tan\left( \frac{2\pi}{7} \right)\]
\[f'\left( x \right) = 1 - e^x \]
\[\text { For f(x) to be increasing, we must have }\]
\[f'\left( x \right) > 0\]
\[ \Rightarrow 1 - e^x > 0\]
\[ \Rightarrow e^x < 1\]
\[ \Rightarrow x < 0\]
\[ \Rightarrow x \in \left( - \infty , 0 \right)\]
\[\text { So,f(x) is increasing on } \left( - \infty , 0 \right) .\]
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