The function f(x) = x2 + 2x - 5 is strictly increasing in the interval:

  1. (-∞, -1)
  2. [-1, ∞)
  3. (-∞, -1]
  4. (-1, ∞)

Answer (Detailed Solution Below)

Option 4 : (-1, ∞)
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Detailed Solution

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Concept:

For a function y = f(x):

  • At the points of local maxima or minima, f'(x) = 0.
  • In the regions where f(x) is increasing, f'(x) > 0.
  • In the regions where f(x) is decreasing, f'(x) < 0.

 

Calculation:

For the function f(x) = x2 + 2x - 5 to be strictly increasing, f'(x) > 0.

⇒ f'(x) = 2x + 2 > 0

⇒ x > -1

⇒ x ∈ (-1, ∞).

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