If $f (x) = 2 e^{x} - a e^{- x} + (2 a + 1) x - 3$ is increasing for all values of x then?

a \in (- \infty, \infty)

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a \in (- \infty, 0]

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a \in [0, \infty)

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None of these

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Solution

The correct option is A $a \in (- \infty, 0]$
For increasing function, $f^{'} (x) > 0$
$f (x) = 2 e^{x} - a e^{- x} + (2 a + 1) x - 3$
$⟹ f^{'} (x) = \frac{2 e^{x}}{i n c r e a s e} + \frac{a e^{- x}}{d e c r e a s e} + (2 a + a) > 0$
So, $a$ must be $- v e$ i.e. $a \in (- \infty, 0]$

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Similar questions

a

f (x) = 2 e^{x} - a e^{- x} + (2 a + 1) x - 3

x

f (x) = a e^{x} - a e^{- x} + (2 a + 1) x - 3

\forall x

f (x) = 2 e^{x} - k e^{- x} + (2 k + 1) x - 3

f (x) = {sin}^{2} x - (2 a + 1) sin x + (a - 3) .

f (x) \leq 0

x ε [0, \frac{π}{2}],

a

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