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MHT CET202312 May 2023Morning ShiftMathematicsApplication of DerivativesActual

The function f (x)= ^4 x+ ^4 x is increasing in

Options

  1. A0 < x < 8
  2. B4 < x < 2
  3. C3 8 < x < 5 8
  4. D5 8 < x < 3 4

Correct answer

B. 4 < x < 2

Step-by-step solution

aligned f (x) & = ^4 x+ ^4 x f ^ (x) & =4 ^3 x x-4 ^3 x x & =4 x x ( ^2 x- ^2 x ) & =+2 2 x 2 x & =- 4 x aligned If f (x) is increasing, then f ^ (x)>0 i.e., aligned - 4 x>0 & < 4 x < 2 & 4 < x < 2 aligned

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