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MHT CET202411 May 2024Morning ShiftMathematicsApplication of DerivativesActual

If f (x)=x^3-6 x^2+9 x+3 is monotonically decreasing function, then x lies in

Options

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

Correct answer

B. (1,3)

Step-by-step solution

array ll & f (x)=x^3-6 x^2+9 x+3 & f ^ (x)=3 x^2-12 x+9 array Since f (x) is monotonically decreasing, aligned & f ^ (x) 0 & 3 x^2-12 x+9 0 & x^2-4 x+3 0 & (x-3)(x-1) 0 & x (1,3) aligned

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