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JEE Main202229 Jun 2022Evening ShiftMathematicsApplication of DerivativesActual

Let f : R → R be a function defined by f x = x - 3 n 1 x - 5 n 2 , n 1 , n 2 ∈ N . The, which of the following is NOT true?

Options

  1. AFor n 1 = 3 ,   n 2 = 4 , there exists α ∈ 3 ,   5 where f attains local maxima.
  2. BFor n 1 = 4 ,   n 2 = 3 , there exists α ∈ 3 ,   5 where f attains local maxima.
  3. CFor n 1 = 3 ,   n 2 = 5 , there exists α ∈ 3 ,   5 where f attains local maxima.
  4. DFor n 1 = 4 ,   n 2 = 6 , there exists α ∈ 3 ,   5 where f attains local maxima.

Correct answer

C. For n 1 = 3 ,   n 2 = 5 , there exists α ∈ 3 ,   5 where f attains local maxima.

Step-by-step solution

Given, f x = x - 3 n 1 x - 5 n 2 Differentiating the function to get maxima and minima, we get f ' x = x - 3 n 1 - 1 x - 5 n 2 - 1 n 1 + n 2 x - 5 n 1 + 3 n 2 n 1 + n 2 Now checking the option, we get Option (3) is incorrect since for n 1 = 3 ,   n 2 = 5 f ' x = 8 x - 3 2 x - 5 4 x - 30 8 minima at x = 30 8 .

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