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The function f(x) = x2 − 2x is strictly decreasing in the interval

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CUET Mathematics 30th Aug 2022 Official Paper
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  1. (−∞, −1)
  2. (−1, ∞)
  3. (−∞, 1)
  4. (1, ∞)

Answer (Detailed Solution Below)

Option 3 : (−∞, 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  to be strictly increasing, f'(x) > 0.

For the function f(x) = x2 − 2x to be strictly decreasing, f'(x) < 0.

⇒ f'(x) = 2x - 2 < 0

⇒ x < 1

⇒ x ∈ (−∞, 1)

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