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BITSAT2009MathematicsApplication of DerivativesActual

The value of (a ) in order that (f(x)= x- x-a x+b ) decreases for all real values is given by

Options

  1. A(a 2 )
  2. Ba ( < 2 )
  3. C(a 1 )
  4. D(a < 1 )

Correct answer

A. (a 2 )

Step-by-step solution

We have; (f(x)= x- x-a x+b ) ( f^ (x)= x+ x-a ) ( f ^ ( x ) < 0 ~ ~ x R ) ( ( x+ x) < a ~ ~ x R ) As the max. value of (( x+ x) ) is ( 2 ) The above is possible when (a 2 )

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