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Find the value of x for which f(x) = x - ex is an increasing function

  1. (0, ∞)
  2. [0, ∞)
  3. (-∞, 0)
  4. None of the above 

Answer (Detailed Solution Below)

Option 3 : (-∞, 0)
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Detailed Solution

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Concept:

  • If f′(x) > 0 then the function is said to be increasing.
  • If f′(x) < 0 then the function is said to be decreasing.

Calculation:

Given:

f(x) = x - ex

Differentiating with respect to x, we get

⇒ f’(x) = 1 - ex

For increasing function,

f'(x) > 0

⇒ 1 – ex > 0

⇒ ex < 1

⇒ ex < e0

∴ x < 0

So, x ∈ (-∞, 0) 

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