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MHT CET202122 Sep 2021Evening ShiftMathematicsApplication of DerivativesActual

The function f(x)= x+6 x 2 x+3 x is increasing, if

Options

  1. A>2
  2. B< 4
  3. C4
  4. D>1

Correct answer

A. >2

Step-by-step solution

aligned & f(x)= x+6 x 2 x+3 x & f^ (x)= [(2 x+3 x)( x-6 x]-[ x+6 x)(2 x-3 x)] (2 x+3 x)^2 aligned When f ^ ( x ) 0 , we get aligned & [ (2 x x +3 ^2 x -12 ^2 x -18 x x ) . & .- (2 x x +12 ^2 x -3 ^2 x -18 sun x x ) ] 0 & 3 ( ^2 x + ^2 x )-12 ( ^2 x + ^2 x ) 0 & 3 -12 0 4 aligned

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