PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
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# Solution for The Interval of Increase of the Function F(X) = X − Ex + Tan (2π/7) is (A) (0, ∞) (B) (−∞, 0) (C) (1, ∞) (D) (−∞, 1) - PUC Karnataka Science Class 12 - Mathematics

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#### Question

The interval of increase of the function f(x) = x − ex + tan (2π/7) is
(a) (0, ∞)
(b) (−∞, 0)
(c) (1, ∞)
(d) (−∞, 1)

#### Solution

(b) (−∞, 0)

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

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

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

$f'\left( x \right) > 0$

$\Rightarrow 1 - e^x > 0$

$\Rightarrow e^x < 1$

$\Rightarrow x < 0$

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

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

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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.
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