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AP EAMCET202124 Aug 2021Morning ShiftMathematicsApplication of DerivativesActual

If f(x)=k x^3-9 x^2+9 x+3(k>0) is increasing for all x , then

Options

  1. Ak 3
  2. Bk 3
  3. C0 < k < 1
  4. D1 < k < 3

Correct answer

B. k 3

Step-by-step solution

f(x)=k x^3-9 x^2+9 x+3(k>0) is increasing for all x . f(x) is increasing, then f^ (x) 0 aligned & f^ (x) 0 & 3 k x^2-18 x+9 0 & k x^2-6 x+3 0 & aligned Using concept of quadratic polynomial for k>0 It is possible only, when aligned & D 0 & b^2-4 a c 0 & (-6)^2-4(k)(3) 0 36-12 k 0 & 12 k 36 k 3 & aligned Solution is k 3 .

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