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JEE Main20245 Apr 2024Morning ShiftMathematicsApplication of DerivativesActual

For the function f(x)= x+3 x- 2 (x^2+x ), where x [0, 2 ], consider the following two statements : (I) f is increasing in (0, 2 ) . (II) f^ is decreasing in (0, 2 ) . Between the above two statements,

Options

  1. Aonly (II) is true.
  2. Bonly (I) is true.
  3. Cneither (I) nor (II) is true.
  4. Dboth (I) and (II) are true

Correct answer

D. both (I) and (II) are true

Step-by-step solution

aligned & f ( x )= x +3 x - 2 ( x ^2+ x ) x [0, 2 ] & f ^ ( x )= x +3- 2 (2 x +1)>0 f ( x ) & f ^ ( x )=- x +0- 2 (2) & =- x - 4 -2 ( +3 2 x +1)>- 2 ( +3 +1) & +ve 3- 2 >3- 2 (2 x+1)>3- 2 ( +ve +1) & aligned

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