Let f :   R → R be a function defined by f x = x - 3 n 1 x - 5 n 2 ,   n 1 ,   n 2…

Let f: R→R be a function defined by fx=x-3n1x-5n2, n1, n2∈N. The, which of the following is NOT true?
  1. For n1=3, n2=4, there exists α∈3, 5 where f attains local maxima.
  2. For n1=4, n2=3, there exists α∈3, 5 where f attains local maxima.
  3. For n1=3, n2=5, there exists α∈3, 5 where f attains local maxima.
  4. For n1=4, n2=6, there exists α∈3, 5 where f attains local maxima.

Solution

Given,

fx=x-3n1x-5n2

Differentiating the function to get maxima and minima, we get

f'x=x-3n1-1x-5n2-1n1+n2x-5n1+3n2n1+n2

Now checking the option, we get

Option (3) is incorrect since

for n1=3, n2=5

f'x=8x-32x-54x-308

minima at x=308.

Asked in: JEE Main 2022 (29 Jun Shift 2)

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