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MHT CET202617 April 2026Morning ShiftMathematicsDifferentiationActual

The derivative of the function f(x) = ^4 x + ^4 x, 0 x 2 is positive for

Options

  1. A0 < x < 8
  2. B4 < x < 2
  3. C2 < x < 5 8
  4. D5 8 < x < 3 4

Correct answer

B. 4 < x < 2

Step-by-step solution

Given f(x) = ^4 x + ^4 x Rewriting the function: f(x) = ( ^2 x + ^2 x)^2 - 2 ^2 x ^2 x f(x) = 1 - 1 2 (2 x x)^2 = 1 - 1 2 ^2(2x) Differentiating with respect to x : f'(x) = - 1 2 2 (2x) (2x) 2 f'(x) = -2 (2x) (2x) = - (4x) For the derivative to be positive, f'(x) > 0 : - (4x) > 0 (4x) The sine function is negative when its argument lies in the intervals ( , 2 ), (3 , 4 ), (5 , 6 ), Taking the first interval: 4 Answer: 4 < x < 2

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