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JEE Main20207 Jan 2020Morning ShiftMathematicsApplication of DerivativesActual

Let the function , f : - 7 , 0 → R be continuous on - 7 , 0 and differentiable on - 7 , 0 . If f - 7 = - 3 and f ' x ≤ 2 for all x ∈ - 7 , 0 , then for all such functions f , f - 1 + f 0 lies in the interval

Options

  1. A- ∞ , 20
  2. B- 3 , 11
  3. C- ∞ , 11
  4. D- 6 , 20

Correct answer

A. - ∞ , 20

Step-by-step solution

Lets use LMVT for x ∈ - 7 , - 1 f - 1 - f - 7 - 1 + 7 ≤ 2 f - 1 + 3 6 ≤ 2 ⇒ f - 1 ≤ 9 Lets use LMVT for x ∈ - 7 , 0 f 0 - f - 7 0 + 7 ≤ 2 f 0 + 3 7 ≤ 2 ⇒ f 0 ≤ 11 ∴ f 0 + f - 1 ≤ 20

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