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BITSAT2016MathematicsApplication of DerivativesActual

The set of all values of a for which the function f(x)= (a²-3 a+2 ) ( ² x / 4- ² x / 4 )+(a-1) x+ 1 does not possess critical points is

Options

  1. A[1, )
  2. B(0,1) (1,4)
  3. C(-2,4)
  4. D(1,3) (3,5)

Correct answer

B. (0,1) (1,4)

Step-by-step solution

(f(x)= (a²=-3 a+2 ) ( ² x / 4- ² x / 4 )+(a-1) x+ 1 ) ( f ( x )=( a -1)( a -2) x / 2+( a -1) x + 1 ) ( f ^ ( x )=- 1 2 ( a -1)( a -2) x 2 +( a -1) ) ( f ^ ( x )=( a -1) [1- ( a -2) 2 x 2 ] ) If (f(x) ) does not possess critical points, then (f^ (x) ) = 0 for any (x R ) ( (a-1) [1- (a-2) 2 x 2 ] ) = 0 for any (x R ) ( a =1 ) and (1- ( a -2 2 ) x 2 =0 ) must not have any solution in ( R ). ( a =1 ) and ( x 2 = 2 a -2 ) is not solvable in ( R ). ( a = 1 ) and ( | 2 a -2 |>1 [ . ) For ( a =2, f ( x )= x + 1 f ^ ( x )=1

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