#### Question

The interval of increase of the function *f*(*x*) = *x* − *e ^{x}* + tan (2π/7) is

(a) (0, ∞)

(b) (−∞, 0)

(c) (1, ∞)

(d) (−∞, 1)

#### Solution

(b) (−∞, 0)

\[f\left( x \right) = x - e^x + \tan\left( \frac{2\pi}{7} \right)\]

\[f'\left( x \right) = 1 - e^x \]

\[\text { Forf(x) to be increasing, we must have }\]

\[f'\left( x \right) > 0\]

\[ \Rightarrow 1 - e^x > 0\]

\[ \Rightarrow e^x < 1\]

\[ \Rightarrow x < 0\]

\[ \Rightarrow x \in \left( - \infty , 0 \right)\]

\[\text { So,f(x)is increasing on } \left( - \infty , 0 \right) .\]

Is there an error in this question or solution?

Solution The Interval of Increase of the Function F(X) = X − Ex + Tan (2π/7) is (A) (0, ∞) (B) (−∞, 0) (C) (1, ∞) (D) (−∞, 1) Concept: Increasing and Decreasing Functions.