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JEE Main20248 Apr 2024Morning ShiftMathematicsApplication of DerivativesActual

For the function f(x)=( x)-x+1, x R , between the following two statements (S1) f(x)=0 for only one value of x in [0, ] . (S2) f(x) is decreasing in [0, 2 ] and increasing in [ 2 , ] .

Options

  1. ABoth (S1) and (S2) are correct.
  2. BBoth (S1) and (S2) are incorrect.
  3. COnly (S2) is correct.
  4. DOnly (S1) is correct.

Correct answer

D. Only (S1) is correct.

Step-by-step solution

aligned & f^ (x)= x-x+1 & f^ (x)=- x-1 aligned f is decreasing x R aligned & f ( x )=0 & f (0)=2, f ( )=- aligned f is strictly decreasing in [0, ] and f (0) . f ( ) < 0 only one solution of f ( x )=0 S 1 is correct and S 2 is incorrect.

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