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JEE Main202124 Feb 2021Evening ShiftMathematicsApplication of DerivativesActual

Let f : R → R be defined as f x = - 55 x , if x < - 5 2 x 3 - 3 x 2 - 120 x , if - 5 ≤ x ≤ 4 2 x 3 - 3 x 2 - 36 x - 336 , if x > 4 Let A = x ∈ R : f is increasing . Then A is equal to:

Options

  1. A- 5 , ∞
  2. B- 5 ,   - 4 ∪ 4 ,   ∞
  3. C- ∞ , - 5 ∪ - 4 , ∞
  4. D- ∞ , - 5 ∪ 4 , ∞

Correct answer

B. - 5 ,   - 4 ∪ 4 ,   ∞

Step-by-step solution

f x = - 55 x , if   x < - 5 2 x 3 - 3 x 2 - 120 x , if - 5 ≤ x ≤ 4 2 x 3 - 3 x 2 - 36 x - 336 , if   x > 4 f ' x = - 55 , if   x < - 5 6 x 2 - 6 x - 120 , if - 5 ≤ x ≤ 4 6 x 2 - 6 x - 36 , if   x > 4 f ' x = - 55 ; x < - 5 6 x - 5 x + 4 ; - 5 < x < 4 6 x - 3 x + 2 ; x > 4 f x is increasing ⇒ f ' x > 0 So, x ∈ - 5 , - 4 ∪ 4 , ∞

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