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MHT CET202416 May 2024Evening ShiftMathematicsApplication of DerivativesActual

If f (x)= a x+b x c x+ d x is decreasing for all x , then

Options

  1. Aad - bc 0
  2. Bad - bc 0
  3. Cab - cd 0
  4. Dab - cd 0

Correct answer

B. ad - bc 0

Step-by-step solution

aligned & f (x)= a x+ b x c x+ d x & f (x) will be decreasing, if f ^ (x) 0 & 1 ( csin x+ d x)^2 [( csin x+ d x)( a x-b x) aligned -(a x+b x)( x-d x)] 0 aligned & acsin x x- bc ^2 x+ ad ^2 x & - bd x x- acsin x x+ ad ^2 x aligned - bc ^2 x+ bdsin x x 0 aligned & ad ( ^2 x+ ^2 x )- bc ( ^2 x+ ^2 x ) 0 & ad - bc 0 aligned

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