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AP EAMCET20228 Jul 2022Evening ShiftMathematicsApplication of DerivativesActual

If f(x)= 3 x- x-2 a x+b decreases for all values of x , then

Options

  1. Aa 1
  2. Ba=1
  3. Ca 1
  4. Da < 1

Correct answer

A. a 1

Step-by-step solution

f(x)= 3 x- x-2 a x+b f^ (x)= 3 x+ x-2 a aligned & =2 ( 3 2 x+ 1 2 x )-2 a & =2 (x+ 3 )-2 a aligned When, f(x) decreases. Then, f^ (x) 0 aligned & 2 (x+ 3 )-2 a 0 & 2 a 2 (x+ 3 ) a (x+ 3 ) aligned aligned & (x+ 3 ) 1 & a 1 aligned

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